9-Multiplicando Polin\303\264mios Estudaremos os m\303\251todos de multiplica\303\247\303\243o de dois polin\303\264mios: m\303\251todo FOIL , f\303\263rmulas de multiplica\303\247\303\243o em casos especiais, e um m\303\251todo geral para multiplicar quaisquer polin\303\264mios e bin\303\264mios de pot\303\252ncia maior. <Text-field style="Heading 1" size="14" layout="Heading 1"><Font size="14" encoding="UTF-8">0. C\303\263digo</Font></Text-field>
restart; with(plots):
Warning, the name changecoords has been redefined
MultiplicandoPolin\303\264mios := proc( poly1, poly2 )
# a = quanity of a, ar = a's rate, and so forth for b
local p1, p2, n1, n2,A, B,R, C,i,j,k ;
p1 := sort( poly1, x); p2 := sort( poly2, x);
n1 := nops(p1); n2 := nops(p2);
R := array([ seq( op(j-1, p1), j = 1..n1+1) ]);
R[1] := 1;
C := array([ seq( op(j-1, p2), j = 1..n2+1) ]);
C[1] := 1;
A := array( [seq( [ seq(C[k]*R[j] , j = 1..n1+1) ],
k = 1..n2+1)]);
A[1,1] := ` `;
B := array( [seq( [ seq( ` ` , j = 1..(n1+2) ) ],
k = 1..(n2+2) )]);
for j from 1 to n1 do B[1, j+2] := A[1,j+1]; od;
for i from 1 to n2 do B[i+2, 1] := A[i+1,1]; od;
for j from 1 to n1 do B[2, j+2] := `__`; od;
for i from 1 to n2 do B[i+2, 2] := `|`; od;
for i from 1 to n2 do
for j from 1 to n1 do
B[i+2,j+2] := A[i+1,j+1];
od;od;
print(B); print(` `);
print(p1*p2 = sort( expand( poly1*poly2), x ));
end proc:
FOIL := proc( poly1, poly2 )
local p1, p2, n1, n2,A, B,R, C,i,j,k, term ;
p1 := sort( poly1, x); p2 := sort( poly2, x);
n1 := nops(p1); n2 := nops(p2);
if( (n1 = 2 ) and (n2 = 2) )
then
term := sort( expand( op(1,p1)*op(1,p2), x ));
print(cat(`F (1\302\272 x 1\302\272) `,(op(1,p1)),`*`,op(1,p2),` = `),term);
term := sort( expand( op(1,p1)*op(2,p2), x ));
print(cat(`O (par externo) `,(op(1,p1)),`*`,op(2,p2),` = `),term);
term := sort( expand( op(2,p1)*op(1,p2), x ));
print(cat(`I (par interno) `,(op(2,p1)),`*`,op(1,p2),` = `),term);
term := sort( expand( op(2,p1)*op(2,p2), x ));
print(cat(`L (\303\272ltimo x \303\272ltimo) `,(op(2,p1)),`*`,op(2,p2),` = `),term);
print(` `);
print(p1*p2 = sort( expand( poly1*poly2), x ));
else
print(`Desculpa,..., FOIL somente funciona para o produto de bin\303\264mios`);
fi;
end proc:
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">1. O produto de Dois Bin\303\264mios - Foil</Font></Text-field> Para multiplicar dois bin\303\264mios, usamos o seguinte m\303\251todo. Multiplicamos :
F : Primeiro x primeiro,
O : Par externo (primeiro x o \303\272ltimo)
I : Par interno (\303\272ltimo x primeiro)
L : \303\232ltimo x \303\272ltimo
Geralmente o segundo e o terceito termo se combinam, pois s\303\243o termos semelhantes, e o resultado ser\303\241 um trin\303\264mio (tr\303\252s termos).
FOIL( x + 2, x + 9);
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FOIL( x + 9, x - 13);
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FOIL( x - 22, x + 18);
NiQlQEZ+figxfGp5fGp2fGh2fnh+MXxqeXxqdnxodil+fn5+fn5+fn54Knh+PX5HKiQpJSJ4RyIiIyIiIg== NiQlPE9+fihwYXJ+ZXh0ZXJubyl+fn5+eCoxOH49fkcsJComIiM9IiIiJSJ4R0YnRic= NiQlP0l+fihwYXJ+aW50ZXJubyl+fn5+fn4tMjIqeH49fkcsJComIiNBIiIiJSJ4R0YnISIi NiQlSEx+fih8anl8anZ8aHZsdGltb354fnxqeXxqdnxodmx0aW1vKX5+fn5+fi0yMioxOH49fkchJCdS NiMlIn5H NiMvKiYsJiUieEciIiIiIz0iIiIiIiIsJiUieEciIiIiI0EhIiIiIiIsKCokKSUieEciIiMiIiIiIiIqJiIiJSIiIiUieEciIiIhIiIiJCdSISIi
FOIL( x - 36, x + 48 );
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FOIL( 7*x + 16, 14*x + 24 );
NiQoKCgoJTpGfn4oMXxqeXxqdnxodn54fjF8anl8anZ8aHYpfn5+fn5+fn5+RywkKiYiIigiIiIlInhHRitGKyUiKkcsJComIiM5RitGLEYrRislJH49fkcsJComIiMpKkYrKUYsIiIjRitGKw== NiQoKCgoJTVPfn4ocGFyfmV4dGVybm8pfn5+fkcsJComIiIoIiIiJSJ4R0YrRislIipHIiNDJSR+PX5HLCQqJiIkbyJGK0YsRitGKw== NiQoKCU6SX5+KHBhcn5pbnRlcm5vKX5+fn5+fjE2KkcsJComIiM5IiIiJSJ4R0YpRiklJH49fkcsJComIiRDI0YpRipGKUYp NiQlR0x+fih8anl8anZ8aHZsdGltb354fnxqeXxqdnxodmx0aW1vKX5+fn5+fjE2KjI0fj1+RyIkJVE= NiMlIn5H NiMvKiYsJiomIiM5IiIiJSJ4RyIiIiIiIiIjQyIiIiIiIiwmKiYiIigiIiIlInhHIiIiIiIiIiM7IiIiIiIiLCgqJiIjKSoiIiIpJSJ4RyIiIyIiIiIiIiomIiQjUiIiIiUieEciIiIiIiIiJCVRIiIi
Aqui vemos uma f\303\263rmula desse m\303\251todo. Entretanto, \303\251 mais f\303\241cil entender o princ\303\255pio:
FOIL( a*x + b, c*x + d);
NiQoKCgoJTpGfn4oMXxqeXxqdnxodn54fjF8anl8anZ8aHYpfn5+fn5+fn5+RyomJSJhRyIiIiUieEdGKiUiKkcqJiUiY0dGKkYrRiolJH49fkcqKEYpRiopRisiIiNGKkYuRio= NiQoKCgoJTVPfn4ocGFyfmV4dGVybm8pfn5+fkcqJiUiYUciIiIlInhHRiolIipHJSJkRyUkfj1+RyooRilGKkYrRipGLUYq NiQoKCU5SX5+KHBhcn5pbnRlcm5vKX5+fn5+fmIqRyomJSJjRyIiIiUieEdGKCUkfj1+RyooRilGKCUiYkdGKEYnRig= NiQlRUx+fih8anl8anZ8aHZsdGltb354fnxqeXxqdnxodmx0aW1vKX5+fn5+fmIqZH49fkcqJiUiYkciIiIlImRHRiY= NiMlIn5H NiMvKiYsJiomJSJjRyIiIiUieEciIiIiIiIlImRHIiIiIiIiLCYqJiUiYUciIiIlInhHIiIiIiIiJSJiRyIiIiIiIiwqKiglImFHIiIiJSJjRyIiIiklInhHIiIjIiIiIiIiKiglImJHIiIiJSJjRyIiIiUieEciIiIiIiIqKCUiYUciIiIlImRHIiIiJSJ4RyIiIiIiIiomJSJiRyIiIiUiZEciIiIiIiI=
Observe que tamb\303\251m podemos multiplicar dois polin\303\264mios em forma de tabela. Colocamos os coeficientes de um bin\303\264mio como cabe\303\247a de uma coluna e os termos do outro bin\303\264mio como cabe\303\247a da outra coluna, e ent\303\243o completamos a tabela de multiplica\303\247\303\243o, e combinando os termos semelhantes.
MultiplicandoPolin\303\264mios( x + 2, 3*x + 9); 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 NiMlIn5H NiMvKiYsJiomIiIkIiIiJSJ4RyIiIiIiIiIiKiIiIiIiIiwmJSJ4RyIiIiIiIyIiIiIiIiwoKiYiIiQiIiIpJSJ4RyIiIyIiIiIiIiomIiM6IiIiJSJ4RyIiIiIiIiIjPSIiIg==
MultiplicandoPolin\303\264mios( 100*x + 8, 120*x + 9); 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 NiMlIn5H NiMvKiYsJiomIiQ/IiIiIiUieEciIiIiIiIiIioiIiIiIiIsJiomIiQrIiIiIiUieEciIiIiIiIiIikiIiIiIiIsKComIiYrPyIiIiIpJSJ4RyIiIyIiIiIiIiomIiVnPSIiIiUieEciIiIiIiIiI3MiIiI=
MultiplicandoPolin\303\264mios( 16*x + 27, 32*x + 9); 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 NiMlIn5H NiMvKiYsJiomIiNLIiIiJSJ4RyIiIiIiIiIiKiIiIiIiIiwmKiYiIzsiIiIlInhHIiIiIiIiIiNGIiIiIiIiLCgqJiIkNyYiIiIpJSJ4RyIiIyIiIiIiIiomIiUzNSIiIiUieEciIiIiIiIiJFYjIiIi
MultiplicandoPolin\303\264mios( .01*x + 2, .03*x + .05); 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 NiMlIn5H NiMvKiYsJiomJCIiJCEiIyIiIiUieEciIiIiIiIkIiImISIjIiIiIiIiLCYqJiQiIiIhIiMiIiIlInhHIiIiIiIiIiIjIiIiIiIiLCgqJiQiIiQhIiUiIiIpJSJ4RyIiIyIiIiIiIiomJCIkMCchIiUiIiIlInhHIiIiIiIiJCIjNSEiIyIiIg== <Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">2. O Produto de Dois Bin\303\264mios - Casos Especiais</Font></Text-field> H\303\241 dois casos especiais que necessitam das suas pr\303\263prias f\303\263rmulas.
Primeiro temos a Diferen\303\247a de Quadrados , ou Produto de coeficiente Conjugados . Isso acontece quando multiplicamos um bin\303\264mio por outro bin\303\264mio que \303\251 quase id\303\252ntico, a n\303\243o ser pelo sinal que \303\251 oposto.
FOIL( x + 2, x - 2 );
NiQlQEZ+figxfGp5fGp2fGh2fnh+MXxqeXxqdnxodil+fn5+fn5+fn54Knh+PX5HKiQpJSJ4RyIiIyIiIg== NiQlPE9+fihwYXJ+ZXh0ZXJubyl+fn5+eCotMn49fkcsJComIiIjIiIiJSJ4R0YnISIi NiQlPUl+fihwYXJ+aW50ZXJubyl+fn5+fn4yKnh+PX5HLCQqJiIiIyIiIiUieEdGJ0Yn NiQlRkx+fih8anl8anZ8aHZsdGltb354fnxqeXxqdnxodmx0aW1vKX5+fn5+fjIqLTJ+PX5HISIl NiMlIn5H NiMvKiYsJiUieEciIiIiIiMhIiIiIiIsJiUieEciIiIiIiMiIiIiIiIsJiokKSUieEciIiMiIiIiIiIiIiUhIiI=
Observeremos que ambos os pares s\303\243o iguais, por\303\251m sim\303\251tricos. Ao combinarmos termos sim\303\251tricos eles s\303\243o cancelados. Logo, a resposta final tem apenas dois termos em vez de tr\303\252s. Vejamos outro exemplo:
FOIL( 11*x + 13 , 11*x - 13);
NiQoKCgoJTpGfn4oMXxqeXxqdnxodn54fjF8anl8anZ8aHYpfn5+fn5+fn5+RywkKiYiIzYiIiIlInhHRitGKyUiKkdGKCUkfj1+RywkKiYiJEAiRispRiwiIiNGK0Yr NiQoKCgoJTVPfn4ocGFyfmV4dGVybm8pfn5+fkcsJComIiM2IiIiJSJ4R0YrRislIipHISM4JSR+PX5HLCQqJiIkViJGK0YsRishIiI= NiQoKCU6SX5+KHBhcn5pbnRlcm5vKX5+fn5+fjEzKkcsJComIiM2IiIiJSJ4R0YpRiklJH49fkcsJComIiRWIkYpRipGKUYp NiQlSEx+fih8anl8anZ8aHZsdGltb354fnxqeXxqdnxodmx0aW1vKX5+fn5+fjEzKi0xM349fkchJHAi NiMlIn5H NiMvKiYsJiomIiM2IiIiJSJ4RyIiIiIiIiIjOCEiIiIiIiwmKiYiIzYiIiIlInhHIiIiIiIiIiM4IiIiIiIiLCYqJiIkQCIiIiIpJSJ4RyIiIyIiIiIiIiIkcCIhIiI= Aha! Aconteceu de novo. Vejamos se encontramos uma f\303\263rmula.
FOIL( x- b, x + b);
NiQlQEZ+figxfGp5fGp2fGh2fnh+MXxqeXxqdnxodil+fn5+fn5+fn54Knh+PX5HKiQpJSJ4RyIiIyIiIg== NiQlO09+fihwYXJ+ZXh0ZXJubyl+fn5+eCpifj1+RyomJSJ4RyIiIiUiYkdGJg== NiQoKCgoJTdJfn4ocGFyfmludGVybm8pfn5+fn5+RywkJSJiRyEiIiUiKkclInhHJSR+PX5HLCQqJkYsIiIiRilGMEYq NiQoKCgoJT9Mfn4ofGp5fGp2fGh2bHRpbW9+eH58anl8anZ8aHZsdGltbyl+fn5+fn5HLCQlImJHISIiJSIqR0YpJSR+PX5HLCQqJClGKSIiIyIiIkYq NiMlIn5H NiMvKiYsJiUieEciIiIlImJHIiIiIiIiLCYlInhHIiIiJSJiRyEiIiIiIiwmKiQpJSJ4RyIiIyIiIiIiIiokKSUiYkciIiMiIiIhIiI=
FOIL( a*x - b, a*x + b );
NiQoKCgoJTpGfn4oMXxqeXxqdnxodn54fjF8anl8anZ8aHYpfn5+fn5+fn5+RyomJSJhRyIiIiUieEdGKiUiKkdGKCUkfj1+RyomKUYpIiIjRiopRitGMEYq NiQoKCgoJTVPfn4ocGFyfmV4dGVybm8pfn5+fkcqJiUiYUciIiIlInhHRiolIipHJSJiRyUkfj1+RyooRilGKkYrRipGLUYq NiQoKCgoJTdJfn4ocGFyfmludGVybm8pfn5+fn5+RywkJSJiRyEiIiUiKkcqJiUiYUciIiIlInhHRi4lJH49fkcsJCooRi1GLkYvRi5GKUYuRio= NiQoKCgoJT9Mfn4ofGp5fGp2fGh2bHRpbW9+eH58anl8anZ8aHZsdGltbyl+fn5+fn5HLCQlImJHISIiJSIqR0YpJSR+PX5HLCQqJClGKSIiIyIiIkYq NiMlIn5H NiMvKiYsJiomJSJhRyIiIiUieEciIiIiIiIlImJHIiIiIiIiLCYqJiUiYUciIiIlInhHIiIiIiIiJSJiRyEiIiIiIiwmKiYpJSJhRyIiIyIiIiklInhHIiIjIiIiIiIiKiQpJSJiRyIiIyIiIiEiIg==
Ent\303\243o, podemos encontrar essa f\303\263rmula fazendo esse tipo de problema. O primeiro termo ao quadrado menos o \303\272ltimo termo ao quadrado. \303\211 simples assim, mas s\303\263 funciona se os dois termos forem exatamente sim\303\251tricos.
(a*x - b)*(a*x + b): % = expand(%);
NiMvKiYsJiomJSJhRyIiIiUieEciIiIiIiIlImJHIiIiIiIiLCYqJiUiYUciIiIlInhHIiIiIiIiJSJiRyEiIiIiIiwmKiYpJSJhRyIiIyIiIiklInhHIiIjIiIiIiIiKiQpJSJiRyIiIyIiIiEiIg==
(3*x - 5)*(3*x + 5): % = expand(%);
NiMvKiYsJiomIiIkIiIiJSJ4RyIiIiIiIiIiJiEiIiIiIiwmKiYiIiQiIiIlInhHIiIiIiIiIiImIiIiIiIiLCYqJiIiKiIiIiklInhHIiIjIiIiIiIiIiNEISIi
(80*x - 66)*(80*x + 66): % = expand(%);
NiMvKiYsJiomIiMhKSIiIiUieEciIiIiIiIiI20hIiIiIiIsJiomIiMhKSIiIiUieEciIiIiIiIiI20iIiIiIiIsJiomIiUrayIiIiklInhHIiIjIiIiIiIiIiVjViEiIg==
Outro caso especial, \303\251 o quadrado perfeito de um bin\303\264mio. Isso \303\251 quando um \303\272nico bin\303\264mio \303\251 elevado ao quadrado.
FOIL( x + 5, x + 5);
NiQlQEZ+figxfGp5fGp2fGh2fnh+MXxqeXxqdnxodil+fn5+fn5+fn54Knh+PX5HKiQpJSJ4RyIiIyIiIg== NiQlO09+fihwYXJ+ZXh0ZXJubyl+fn5+eCo1fj1+RywkKiYiIiYiIiIlInhHRidGJw== NiQlPUl+fihwYXJ+aW50ZXJubyl+fn5+fn41Knh+PX5HLCQqJiIiJiIiIiUieEdGJ0Yn NiQlRUx+fih8anl8anZ8aHZsdGltb354fnxqeXxqdnxodmx0aW1vKX5+fn5+fjUqNX49fkciI0Q= NiMlIn5H NiMvKiQpLCYlInhHIiIiIiImIiIiIiIjIiIiLCgqJCklInhHIiIjIiIiIiIiKiYiIzUiIiIlInhHIiIiIiIiIiNEIiIi
MultiplicandoPolin\303\264mios( 19*x - 3, 19*x - 3); 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 NiMlIn5H NiMvKiQpLCYqJiIjPiIiIiUieEciIiIiIiIiIiQhIiIiIiMiIiIsKComIiRoJCIiIiklInhHIiIjIiIiIiIiKiYiJDkiIiIiJSJ4RyIiIiEiIiIiKiIiIg==
Perceba que os dois bin\303\264mios s\303\243o iguais, temos o mesmo termo duas vezes. Ent\303\243o vejamos a f\303\263rmula esse caso.
MultiplicandoPolin\303\264mios( a*x + b, a*x + b); 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 NiMlIn5H NiMvKiQpLCYqJiUiYUciIiIlInhHIiIiIiIiJSJiRyIiIiIiIyIiIiwoKiYpJSJhRyIiIyIiIiklInhHIiIjIiIiIiIiKioiIiMiIiIlImFHIiIiJSJiRyIiIiUieEciIiIiIiIqJCklImJHIiIjIiIiIiIi
Parece que quando elevamos o primeiro e o segundo termo ao quadrado dobramos os coeficientes, ent\303\243o dobramos o produto dos coeficientes.
MultiplicandoPolin\303\264mios( 3*x + 4, 3*x + 4); 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 NiMlIn5H NiMvKiQpLCYqJiIiJCIiIiUieEciIiIiIiIiIiUiIiIiIiMiIiIsKComIiIqIiIiKSUieEciIiMiIiIiIiIqJiIjQyIiIiUieEciIiIiIiIiIzsiIiI=
MultiplicandoPolin\303\264mios( 100*x - 8, 100*x - 8); 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 NiMlIn5H NiMvKiQpLCYqJiIkKyIiIiIlInhHIiIiIiIiIiIpISIiIiIjIiIiLCgqJiImKysiIiIiKSUieEciIiMiIiIiIiIqJiIlKzsiIiIlInhHIiIiISIiIiNrIiIi
Perceba a diferen\303\247a entre uma constante negativa e uma constante positiva. A \303\272nica diferen\303\247a \303\251 que o sinal do termo do meio \303\251 o mesmo sinal do bin\303\264mio do termo constante.
( 2*x - 5)*(2*x - 5): % = expand(%);
( 2*x + 5)*(2*x + 5): % = expand(%);
NiMvKiQpLCYqJiIiIyIiIiUieEciIiIiIiIiIiYhIiIiIiMiIiIsKComIiIlIiIiKSUieEciIiMiIiIiIiIqJiIjPyIiIiUieEciIiIhIiIiI0QiIiI= NiMvKiQpLCYqJiIiIyIiIiUieEciIiIiIiIiIiYiIiIiIiMiIiIsKComIiIlIiIiKSUieEciIiMiIiIiIiIqJiIjPyIiIiUieEciIiIiIiIiI0QiIiI=
( 37*x - 17)*(37*x - 17): % = expand(%);
( 37*x + 17)*(37*x + 17): % = expand(%);
NiMvKiQpLCYqJiIjUCIiIiUieEciIiIiIiIiIzwhIiIiIiMiIiIsKComIiVwOCIiIiklInhHIiIjIiIiIiIiKiYiJWU3IiIiJSJ4RyIiIiEiIiIkKkciIiI= NiMvKiQpLCYqJiIjUCIiIiUieEciIiIiIiIiIzwiIiIiIiMiIiIsKComIiVwOCIiIiklInhHIiIjIiIiIiIiKiYiJWU3IiIiJSJ4RyIiIiIiIiIkKkciIiI=
( 1072*x - 232)*(1072*x - 232): % = expand(%);
( 1072*x + 232)*(1072*x + 232): % = expand(%);
NiMvKiQpLCYqJiIlczUiIiIlInhHIiIiIiIiIiRLIyEiIiIiIyIiIiwoKiYiKCU9XDYiIiIpJSJ4RyIiIyIiIiIiIiomIiczdVwiIiIlInhHIiIiISIiIiZDUSYiIiI= NiMvKiQpLCYqJiIlczUiIiIlInhHIiIiIiIiIiRLIyIiIiIiIyIiIiwoKiYiKCU9XDYiIiIpJSJ4RyIiIyIiIiIiIiomIiczdVwiIiIlInhHIiIiIiIiIiZDUSYiIiI= <Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">3. O Produto de Dois Polin\303\264mios Quaisquer</Font></Text-field>
Temos estudado m\303\251todos de resolu\303\247\303\243o de dois bin\303\264mios, mas tamb\303\251m podemos utilizar tabelas para multiplica\303\247\303\243o de polin\303\264mios. Assim como antes, escrevemos cada coeficiente de um polin\303\264mio na esquerda e os outros termos acima. Cada coeficiente tem sua pr\303\263pria linha ou coluna. N\303\263s simplesmente combinamos todos os termos, como em uma tabuada e combinamos os termos semelhantes para encontrar uma resposta.
MultiplicandoPolin\303\264mios( 6*x + 5, 2*x + 11); LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYmLUYjNiUtSSdtdGFibGVHRiQ2OC1JJG10ckdGJDYpLUkkbXRkR0YkNigtSSNtaUdGJDYlUSRgfmBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSlyb3dhbGlnbkdRIUYnLyUsY29sdW1uYWxpZ25HRkUvJStncm91cGFsaWduR0ZFLyUocm93c3BhbkdRIjFGJy8lK2NvbHVtbnNwYW5HRkxGNi1GNzYoLUYjNiYtSSNtbkdGJDYkUSI2RicvRkFRJ25vcm1hbEYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRlcvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRmluLyUpc3RyZXRjaHlHRmluLyUqc3ltbWV0cmljR0Zpbi8lKGxhcmdlb3BHRmluLyUubW92YWJsZWxpbWl0c0dGaW4vJSdhY2NlbnRHRmluLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGaG8tRjo2JVEieEYnRj1GQEZXRkNGRkZIRkpGTS1GNzYoLUZUNiRRIjVGJ0ZXRkNGRkZIRkpGTUZDRkZGSC1GNDYpRjZGNi1GNzYoLUY6NiVRI19fRidGPUZARkNGRkZIRkpGTUZlcEZDRkZGSC1GNDYpLUY3NigtRiM2Ji1GVDYkUSIyRidGV0ZZRltwRldGQ0ZGRkhGSkZNLUY3NigtRjo2JVEkYHxncmBGJ0Y9RkBGQ0ZGRkhGSkZNLUY3NigtRiM2Ji1GVDYkUSMxMkYnRldGWS1JJW1zdXBHRiQ2JUZbcEZgcS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGV0ZDRkZGSEZKRk0tRjc2KC1GIzYmLUZUNiRRIzEwRidGV0ZZRltwRldGQ0ZGRkhGSkZNRkNGRkZILUY0NiktRjc2KC1GVDYkUSMxMUYnRldGQ0ZGRkhGSkZNRmNxLUY3NigtRiM2Ji1GVDYkUSM2NkYnRldGWUZbcEZXRkNGRkZIRkpGTS1GNzYoLUZUNiRRIzU1RidGV0ZDRkZGSEZKRk1GQ0ZGRkgvJSZhbGlnbkdRJWF4aXNGJy9GRFEpYmFzZWxpbmVGJy9GR1EnY2VudGVyRicvRklRJ3xmcmxlZnR8aHJGJy8lL2FsaWdubWVudHNjb3BlR0Y/LyUsY29sdW1ud2lkdGhHUSVhdXRvRicvJSZ3aWR0aEdGXHUvJStyb3dzcGFjaW5nR1EmMS4wZXhGJy8lLmNvbHVtbnNwYWNpbmdHUSYwLjhlbUYnLyUpcm93bGluZXNHUSVub25lRicvJSxjb2x1bW5saW5lc0dGZ3UvJSZmcmFtZUdGZ3UvJS1mcmFtZXNwYWNpbmdHUSwwLjRlbX4wLjVleEYnLyUqZXF1YWxyb3dzR0Zpbi8lLWVxdWFsY29sdW1uc0dGaW4vJS1kaXNwbGF5c3R5bGVHRmluLyUlc2lkZUdRJnJpZ2h0RicvJTBtaW5sYWJlbHNwYWNpbmdHRmR1LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0ZXRlcvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGanZGVw== NiMlIn5H NiMvKiYsJiomIiIjIiIiJSJ4RyIiIiIiIiIjNiIiIiIiIiwmKiYiIiciIiIlInhHIiIiIiIiIiImIiIiIiIiLCgqJiIjNyIiIiklInhHIiIjIiIiIiIiKiYiI3ciIiIlInhHIiIiIiIiIiNiIiIi
MultiplicandoPolin\303\264mios( x^2 + 7*x + 2, 3*x - 8); 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 NiMlIn5H NiMvKiYsJiomIiIkIiIiJSJ4RyIiIiIiIiIiKSEiIiIiIiwoKiQpJSJ4RyIiIyIiIiIiIiomIiIoIiIiJSJ4RyIiIiIiIiIiIyIiIiIiIiwqKiYiIiQiIiIpJSJ4RyIiJCIiIiIiIiomIiM4IiIiKSUieEciIiMiIiIiIiIqJiIjXSIiIiUieEciIiIhIiIiIzshIiI=
MultiplicandoPolin\303\264mios( x + 2, x^2 + 3*x + 9); LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYmLUYjNiUtSSdtdGFibGVHRiQ2OS1JJG10ckdGJDYpLUkkbXRkR0YkNigtSSNtaUdGJDYlUSRgfmBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSlyb3dhbGlnbkdRIUYnLyUsY29sdW1uYWxpZ25HRkUvJStncm91cGFsaWduR0ZFLyUocm93c3BhbkdRIjFGJy8lK2NvbHVtbnNwYW5HRkxGNi1GNzYoLUY6NiVRInhGJ0Y9RkBGQ0ZGRkhGSkZNLUY3NigtSSNtbkdGJDYkUSIyRicvRkFRJ25vcm1hbEYnRkNGRkZIRkpGTUZDRkZGSC1GNDYpRjZGNi1GNzYoLUY6NiVRI19fRidGPUZARkNGRkZIRkpGTUZobkZDRkZGSC1GNDYpLUY3NigtRiM2JC1JJW1zdXBHRiQ2JUZRRlYvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRlpGQ0ZGRkhGSkZNLUY3NigtRjo2JVEkYHxncmBGJ0Y9RkBGQ0ZGRkhGSkZNLUY3NigtRiM2JC1GZG82JUZRLUZXNiRRIjNGJ0ZaRmZvRlpGQ0ZGRkhGSkZNLUY3NigtRiM2JkZWLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRlovJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRmFxLyUpc3RyZXRjaHlHRmFxLyUqc3ltbWV0cmljR0ZhcS8lKGxhcmdlb3BHRmFxLyUubW92YWJsZWxpbWl0c0dGYXEvJSdhY2NlbnRHRmFxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGYHJGY29GWkZDRkZGSEZKRk1GQ0ZGRkgtRjQ2KS1GNzYoLUYjNiZGZHBGW3FGUUZaRkNGRkZIRkpGTUZpby1GNzYoLUYjNiZGZHBGW3FGY29GWkZDRkZGSEZKRk0tRjc2KC1GIzYmLUZXNiRRIjZGJ0ZaRltxRlFGWkZDRkZGSEZKRk1GQ0ZGRkgtRjQ2KS1GNzYoLUZXNiRRIjlGJ0ZaRkNGRkZIRkpGTUZpby1GNzYoLUYjNiZGaHNGW3FGUUZaRkNGRkZIRkpGTS1GNzYoLUZXNiRRIzE4RidGWkZDRkZGSEZKRk1GQ0ZGRkgvJSZhbGlnbkdRJWF4aXNGJy9GRFEpYmFzZWxpbmVGJy9GR1EnY2VudGVyRicvRklRJ3xmcmxlZnR8aHJGJy8lL2FsaWdubWVudHNjb3BlR0Y/LyUsY29sdW1ud2lkdGhHUSVhdXRvRicvJSZ3aWR0aEdGYXUvJStyb3dzcGFjaW5nR1EmMS4wZXhGJy8lLmNvbHVtbnNwYWNpbmdHUSYwLjhlbUYnLyUpcm93bGluZXNHUSVub25lRicvJSxjb2x1bW5saW5lc0dGXHYvJSZmcmFtZUdGXHYvJS1mcmFtZXNwYWNpbmdHUSwwLjRlbX4wLjVleEYnLyUqZXF1YWxyb3dzR0ZhcS8lLWVxdWFsY29sdW1uc0dGYXEvJS1kaXNwbGF5c3R5bGVHRmFxLyUlc2lkZUdRJnJpZ2h0RicvJTBtaW5sYWJlbHNwYWNpbmdHRml1LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0ZaRlovJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGX3dGWg== NiMlIn5H NiMvKiYsKCokKSUieEciIiMiIiIiIiIqJiIiJCIiIiUieEciIiIiIiIiIioiIiIiIiIsJiUieEciIiIiIiMiIiIiIiIsKiokKSUieEciIiQiIiIiIiIqJiIiJiIiIiklInhHIiIjIiIiIiIiKiYiIzoiIiIlInhHIiIiIiIiIiM9IiIi
MultiplicandoPolin\303\264mios( x^2 +7*x - 13, 5*x^2 + 6*x + 4); 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 NiMlIn5H NiMvKiYsKComIiImIiIiKSUieEciIiMiIiIiIiIqJiIiJyIiIiUieEciIiIiIiIiIiUiIiIiIiIsKCokKSUieEciIiMiIiIiIiIqJiIiKCIiIiUieEciIiIiIiIiIzghIiIiIiIsLComIiImIiIiKSUieEciIiUiIiIiIiIqJiIjVCIiIiklInhHIiIkIiIiIiIiKiYiIz4iIiIpJSJ4RyIiIyIiIiEiIiomIiNdIiIiJSJ4RyIiIiEiIiIjXyEiIg==
MultiplicandoPolin\303\264mios( x^3 -10*x^2 + 11*x - 9, 10*x^2 + 17*x + 11); 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 NiMlIn5H NiMvKiYsKComIiM1IiIiKSUieEciIiMiIiIiIiIqJiIjPCIiIiUieEciIiIiIiIiIzYiIiIiIiIsKiokKSUieEciIiQiIiIiIiIqJiIjNSIiIiklInhHIiIjIiIiISIiKiYiIzYiIiIlInhHIiIiIiIiIiIqISIiIiIiLC4qJiIjNSIiIiklInhHIiImIiIiIiIiKiYiIyQpIiIiKSUieEciIiUiIiIhIiIqJiIjXCIiIiklInhHIiIkIiIiISIiKiYiIzgiIiIpJSJ4RyIiIyIiIiEiIiomIiNLIiIiJSJ4RyIiIiEiIiIjKiohIiI=
MultiplicandoPolin\303\264mios( x^3 - 13*x^2 + 6*x + 4, x^3 -8*x^2 - 6*x + 3); 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 NiMlIn5H NiMvKiYsKiokKSUieEciIiQiIiIiIiIqJiIiKSIiIiklInhHIiIjIiIiISIiKiYiIiciIiIlInhHIiIiISIiIiIkIiIiIiIiLCoqJCklInhHIiIkIiIiIiIiKiYiIzgiIiIpJSJ4RyIiIyIiIiEiIiomIiInIiIiJSJ4RyIiIiIiIiIiJSIiIiIiIiwwKiQpJSJ4RyIiJyIiIiIiIiomIiNAIiIiKSUieEciIiYiIiIhIiIqJiIkLyIiIiIpJSJ4RyIiJSIiIiIiIiomIiNQIiIiKSUieEciIiQiIiIiIiIqJiIkMiIiIiIpJSJ4RyIiIyIiIiEiIiomIiInIiIiJSJ4RyIiIiEiIiIjNyIiIg==
MultiplicandoPolin\303\264mios( x^4 + 2*x^3 - 4*x^2 + 8*x - 16, x - 1); 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 NiMlIn5H NiMvKiYsJiUieEciIiIiIiIhIiIiIiIsLCokKSUieEciIiUiIiIiIiIqJiIiIyIiIiklInhHIiIkIiIiIiIiKiYiIiUiIiIpJSJ4RyIiIyIiIiEiIiomIiIpIiIiJSJ4RyIiIiIiIiIjOyEiIiIiIiwuKiQpJSJ4RyIiJiIiIiIiIiokKSUieEciIiUiIiIiIiIqJiIiJyIiIiklInhHIiIkIiIiISIiKiYiIzciIiIpJSJ4RyIiIyIiIiIiIiomIiNDIiIiJSJ4RyIiIiEiIiIjOyIiIg==
Temos aqui um caso interessante.
MultiplicandoPolin\303\264mios( x^4 + x^3 + x^2 + x + 1, x - 1); 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 NiMlIn5H NiMvKiYsJiUieEciIiIiIiIhIiIiIiIsLCokKSUieEciIiUiIiIiIiIqJCklInhHIiIkIiIiIiIiKiQpJSJ4RyIiIyIiIiIiIiUieEciIiIiIiIiIiIiIiIsJiokKSUieEciIiYiIiIiIiIiIiIhIiI=
E mais um.
MultiplicandoPolin\303\264mios( x^4 - x^3 + x^2 - x + 1, x + 1); 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 NiMlIn5H NiMvKiYsJiUieEciIiIiIiIiIiIiIiIsLCokKSUieEciIiUiIiIiIiIqJCklInhHIiIkIiIiISIiKiQpJSJ4RyIiIyIiIiIiIiUieEchIiIiIiIiIiIiIiIsJiokKSUieEciIiYiIiIiIiIiIiIiIiI= <Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">4. Pot\303\252ncias Maiores de Bin\303\264mios</Font></Text-field>
Podemos tamb\303\251m encontrar pot\303\252ncias maiores de bin\303\264mios. Se elevarmos um bin\303\264mio ao quadrado, e depois multiplicarmos o resultado pelo bin\303\264mio novamente, teremos o cubo.
A := 2*x + 3;
MultiplicandoPolin\303\264mios( A, A);
MultiplicandoPolin\303\264mios( A, A^2);
A^3: % = expand(%);
NiM+JSJBRywmKiYiIiMiIiIlInhHIiIiIiIiIiIkIiIi 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 NiMlIn5H NiMvKiQpLCYqJiIiIyIiIiUieEciIiIiIiIiIiQiIiIiIiMiIiIsKComIiIlIiIiKSUieEciIiMiIiIiIiIqJiIjNyIiIiUieEciIiIiIiIiIioiIiI= 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 NiMlIn5H NiMvKiQpLCYqJiIiIyIiIiUieEciIiIiIiIiIiQiIiIiIiQiIiIsKiomIiIpIiIiKSUieEciIiQiIiIiIiIqJiIjTyIiIiklInhHIiIjIiIiIiIiKiYiI2EiIiIlInhHIiIiIiIiIiNGIiIi NiMvKiQpLCYqJiIiIyIiIiUieEciIiIiIiIiIiQiIiIiIiQiIiIsKiomIiIpIiIiKSUieEciIiQiIiIiIiIqJiIjTyIiIiklInhHIiIjIiIiIiIiKiYiI2EiIiIlInhHIiIiIiIiIiNGIiIi
A := 8*x - 7;
MultiplicandoPolin\303\264mios( A, A);
MultiplicandoPolin\303\264mios( A, A^2);
A^3: % = expand(%);
NiM+JSJBRywmKiYiIikiIiIlInhHIiIiIiIiIiIoISIi 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 NiMlIn5H NiMvKiQpLCYqJiIiKSIiIiUieEciIiIiIiIiIighIiIiIiMiIiIsKComIiNrIiIiKSUieEciIiMiIiIiIiIqJiIkNyIiIiIlInhHIiIiISIiIiNcIiIi 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 NiMlIn5H NiMvKiQpLCYqJiIiKSIiIiUieEciIiIiIiIiIighIiIiIiQiIiIsKiomIiQ3JiIiIiklInhHIiIkIiIiIiIiKiYiJVc4IiIiKSUieEciIiMiIiIhIiIqJiIldzYiIiIlInhHIiIiIiIiIiRWJCEiIg== NiMvKiQpLCYqJiIiKSIiIiUieEciIiIiIiIiIighIiIiIiQiIiIsKiomIiQ3JiIiIiklInhHIiIkIiIiIiIiKiYiJVc4IiIiKSUieEciIiMiIiIhIiIqJiIldzYiIiIlInhHIiIiIiIiIiRWJCEiIg==
A := 44*x + 63;
MultiplicandoPolin\303\264mios( A, A);
MultiplicandoPolin\303\264mios( A, A^2);
A^3: % = expand(%);
NiM+JSJBRywmKiYiI1ciIiIlInhHIiIiIiIiIiNqIiIi 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 NiMlIn5H NiMvKiQpLCYqJiIjVyIiIiUieEciIiIiIiIiI2oiIiIiIiMiIiIsKComIiVPPiIiIiklInhHIiIjIiIiIiIiKiYiJVdiIiIiJSJ4RyIiIiIiIiIlcFIiIiI= 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 NiMlIn5H NiMvKiQpLCYqJiIjVyIiIiUieEciIiIiIiIiI2oiIiIiIiQiIiIsKiomIiYlPSYpIiIiKSUieEciIiQiIiIiIiIqJiInL2ZPIiIiKSUieEciIiMiIiIiIiIqJiInM1JfIiIiJSJ4RyIiIiIiIiInWitEIiIi NiMvKiQpLCYqJiIjVyIiIiUieEciIiIiIiIiI2oiIiIiIiQiIiIsKiomIiYlPSYpIiIiKSUieEciIiQiIiIiIiIqJiInL2ZPIiIiKSUieEciIiMiIiIiIiIqJiInM1JfIiIiJSJ4RyIiIiIiIiInWitEIiIi
Podemos tamb\303\251m calcular a quarta pot\303\252ncia da mesma forma.
A := x + 5;
MultiplicandoPolin\303\264mios( A, A);
MultiplicandoPolin\303\264mios( A^2, A^2);
A^4: % = expand(%);
NiM+JSJBRywmJSJ4RyIiIiIiJiIiIg== 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 NiMlIn5H NiMvKiQpLCYlInhHIiIiIiImIiIiIiIjIiIiLCgqJCklInhHIiIjIiIiIiIiKiYiIzUiIiIlInhHIiIiIiIiIiNEIiIi 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 NiMlIn5H NiMvKiQpLCYlInhHIiIiIiImIiIiIiIlIiIiLCwqJCklInhHIiIlIiIiIiIiKiYiIz8iIiIpJSJ4RyIiJCIiIiIiIiomIiRdIiIiIiklInhHIiIjIiIiIiIiKiYiJCsmIiIiJSJ4RyIiIiIiIiIkRCciIiI= NiMvKiQpLCYlInhHIiIiIiImIiIiIiIlIiIiLCwqJCklInhHIiIlIiIiIiIiKiYiIz8iIiIpJSJ4RyIiJCIiIiIiIiomIiRdIiIiIiklInhHIiIjIiIiIiIiKiYiJCsmIiIiJSJ4RyIiIiIiIiIkRCciIiI=
A := 3*x + 7;
MultiplicandoPolin\303\264mios( A, A);
MultiplicandoPolin\303\264mios( A^2, A^2);
A^4: % = expand(%);
NiM+JSJBRywmKiYiIiQiIiIlInhHIiIiIiIiIiIoIiIi 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 NiMlIn5H NiMvKiQpLCYqJiIiJCIiIiUieEciIiIiIiIiIigiIiIiIiMiIiIsKComIiIqIiIiKSUieEciIiMiIiIiIiIqJiIjVSIiIiUieEciIiIiIiIiI1wiIiI= 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 NiMlIn5H NiMvKiQpLCYqJiIiJCIiIiUieEciIiIiIiIiIigiIiIiIiUiIiIsLComIiMiKSIiIiklInhHIiIlIiIiIiIiKiYiJGMoIiIiKSUieEciIiQiIiIiIiIqJiIlWUUiIiIpJSJ4RyIiIyIiIiIiIiomIiU7VCIiIiUieEciIiIiIiIiJSxDIiIi NiMvKiQpLCYqJiIiJCIiIiUieEciIiIiIiIiIigiIiIiIiUiIiIsLComIiMiKSIiIiklInhHIiIlIiIiIiIiKiYiJGMoIiIiKSUieEciIiQiIiIiIiIqJiIlWUUiIiIpJSJ4RyIiIyIiIiIiIiomIiU7VCIiIiUieEciIiIiIiIiJSxDIiIi
e tamb\303\251m podemos calcular pot\303\252ncia maiores da mesma forma. Por exemplo:
A := x + 3;
MultiplicandoPolin\303\264mios( A, A);
MultiplicandoPolin\303\264mios( A^2, A^2);
MultiplicandoPolin\303\264mios( A^4, A);
NiM+JSJBRywmJSJ4RyIiIiIiJCIiIg== 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 NiMlIn5H NiMvKiQpLCYlInhHIiIiIiIkIiIiIiIjIiIiLCgqJCklInhHIiIjIiIiIiIiKiYiIiciIiIlInhHIiIiIiIiIiIqIiIi 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 NiMlIn5H NiMvKiQpLCYlInhHIiIiIiIkIiIiIiIlIiIiLCwqJCklInhHIiIlIiIiIiIiKiYiIzciIiIpJSJ4RyIiJCIiIiIiIiomIiNhIiIiKSUieEciIiMiIiIiIiIqJiIkMyIiIiIlInhHIiIiIiIiIiMiKSIiIg== 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 NiMlIn5H NiMvKiQpLCYlInhHIiIiIiIkIiIiIiImIiIiLC4qJCklInhHIiImIiIiIiIiKiYiIzoiIiIpJSJ4RyIiJSIiIiIiIiomIiMhKiIiIiklInhHIiIkIiIiIiIiKiYiJHEjIiIiKSUieEciIiMiIiIiIiIqJiIkMCUiIiIlInhHIiIiIiIiIiRWIyIiIg==
A := x - 1;
MultiplicandoPolin\303\264mios( A, A);
MultiplicandoPolin\303\264mios( A^2, A^2);
MultiplicandoPolin\303\264mios( A^4, A^4);
NiM+JSJBRywmJSJ4RyIiIiIiIiEiIg== 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 NiMlIn5H NiMvKiQpLCYlInhHIiIiIiIiISIiIiIjIiIiLCgqJCklInhHIiIjIiIiIiIiKiYiIiMiIiIlInhHIiIiISIiIiIiIiIi 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 NiMlIn5H NiMvKiQpLCYlInhHIiIiIiIiISIiIiIlIiIiLCwqJCklInhHIiIlIiIiIiIiKiYiIiUiIiIpJSJ4RyIiJCIiIiEiIiomIiInIiIiKSUieEciIiMiIiIiIiIqJiIiJSIiIiUieEciIiIhIiIiIiIiIiI= 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 NiMlIn5H NiMvKiQpLCYlInhHIiIiIiIiISIiIiIpIiIiLDQqJCklInhHIiIpIiIiIiIiKiYiIikiIiIpJSJ4RyIiKCIiIiEiIiomIiNHIiIiKSUieEciIiciIiIiIiIqJiIjYyIiIiklInhHIiImIiIiISIiKiYiI3EiIiIpJSJ4RyIiJSIiIiIiIiomIiNjIiIiKSUieEciIiQiIiIhIiIqJiIjRyIiIiklInhHIiIjIiIiIiIiKiYiIikiIiIlInhHIiIiISIiIiIiIiIi