Question

Desenvolva utilizando a fórmula de Newton: (x+2)^4
(Binomio de Newton)​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf{(x + y)^n = \dbinom{n}{0}\:.\:x^{n} + \dbinom{n}{1}\:.\:x^{n-1}\:.\:y + ... + \dbinom{n}{k}\:.\:x^{n-k}\:.\:y^k + ... + \dbinom{n}{n}\:.\:y^k}$

$\mathsf{(x + 2)^4 = \dbinom{4}{0}\:.\:x^4 + \dbinom{4}{1}\:.\:x^3\:.\:2 + \dbinom{4}{2}\:.\:x^2\:.\:2^2 + \dbinom{4}{3}\:.\:x\:.\:2^3 + \dbinom{4}{4}\:.\:2^4}$

$\mathsf{(x + 2)^4 = C_{\:4,0}\:.\:x^4 + C_{\:4,1}\:.\:x^3\:.\:2 + C_{\:4,2}\:.\:x^2\:.\:4 + C_{\:4,3}\:.\:x\:.\:8 + C_{\:4,4}\:.\:16}$

$\mathsf{(x + 2)^4 = 1\:.\:x^4 + 4\:.\:x^3\:.\:2 + 6\:.\:x^2\:.\:4 + 4\:.\:x\:.\:8 + 1\:.\:16}$

$\boxed{\boxed{\mathsf{(x + 2)^4 = x^4 + 8x^3 + 24x^2 + 32x + 16}}}$