Question

O desenvolvimento do binômio abaixo é:
(x+2)⁵ 

(a) x5+32
(b) x5=5x4+10x2+5x+32
(c) x5+10x2+5x+32
(d)x5-10x4+40x8-80x-32
(e) n.d.a

AJUDA RAPIDOOOO

Answer 1

Resposta:

${x}^{5} + 10 {x}^{4} + 40 {x}^{3} + 80 {x}^{2} + 80x + 32$

Explicação passo-a-passo:

$(x + 2) ^{5} = \binom{5}{0} {x}^{5 }2 ^{0} + \binom{5}{1} {x}^{4} {2}^{1} + \binom{5}{2} {x}^{3} {2}^{2} + \binom{5}{3} {x}^{2} {2}^{3} + \binom{5}{4} {x}^{1} {2}^{4} + \binom{5}{5} {x}^{0} {2}^{5} =$

$\frac{5!}{0!(5 - 0)!} {x}^{5} + \frac{5!}{1!(5 - 1)!} {x}^{4} 2 + \frac{5!}{2!(5 - 2)!} {x}^{3} {2}^{2} + \frac{5!}{3!(5 - 3)!} {x}^{2} {2}^{3} + \frac{5!}{4!(5 - 4)!} {x} {2}^{4} + \frac{5!}{5!(5 - 5)!} {2}^{5} =$

$\frac{5!}{0! \times 5!} {x}^{5} + \frac{5!}{1! \times 4!} {x}^{4} 2 + \frac{5!}{2! \times 3!} {x}^{3} {2}^{2} + \frac{5!}{3!\times 2!} {x}^{2} {2}^{3} + \frac{5!}{4! \times 1!} x {2}^{4} + \frac{5!}{5! \times 0!} {2}^{5} =$

$\frac{1}{0!} {x}^{5} + \frac{5}{1!} {x}^{4} 2 + \frac{20}{2!} {x}^{3} {2}^{2} + \frac{20}{2!} {x}^{2} {2}^{3} + \frac{5}{1!} x {2}^{4} + \frac{1}{0!} {2}^{5} =$

$1 {x}^{5} + 5 \times 2 {x}^{4} + 10 \times {2}^{2} {x}^{3} + 10 \times {2}^{3} {x}^{2} + 5 \times {2}^{4} x + 1 \times {2}^{5} =$

${x}^{5} + 10 {x}^{4} + 40 {x}^{3} + 80 {x}^{2} + 80x + 32$