Question

Simplificando a expressão (x + 1)(x2 − x + 1) + (2x − 2)(4x2 + 4x + 4) + (x − 1)3, obtém-se:

Answer 1

x^3-x^2+x+x^2-x+1+8x^3+8x^2+8x-8x^2--8x-8+3x-3~=9x3+3x-2

Answer 2

Resposta:

10x3 − 3x2 + 3x − 8.

Explicação passo-a-passo:

Como:  

x3 + y3 = (x + y)(x2 − xy + y2)

e

(x − y)3 = x3 − 3x2y + 3xy3 − y3

Tem-se:

(x + 1)(x2 − x + 1) = x3 + 1

(2x − 2)(4x2 + 4x + 4) = (2x)3 − 23 = 8x3 − 8

(x − 1)3 = x3 − 3x2 + 3x − 1

Portanto:

(x3 + 1) + (8x3 − 8) + (x3 − 3x2 + 3x − 1) = 10x3 − 3x2 + 3x − 8