Question

Um dos fatores da expressão x^2-y^2+(x+y+1)^2-1 é:

A) x-y
B) x-1
C) x+y+1
D) x-y-1
E) x+1

Answer 1

Olá!

$\\ \mathsf{x^2 - y^2 + (x + y + 1)^2 - 1 =} \\\\ \mathsf{(x^2 - y^2) + \left [ (x + y + 1) + 1 \right ] \cdot \left [ (x + y + 1) - 1 \right ] =} \\\\ \mathsf{(x + y) \cdot (x - y) + (x + y + 1 + 1) \cdot (x + y + 1 - 1) =} \\\\ \mathsf{(x + y)(x - y) + (x + y + 2)(x + y) =} \\\\ \mathsf{(x + y) \cdot \left [ (x - y) + (x + y + 2) \right ] =} \\\\ \mathsf{(x + y)(x - y + x + y + 2) =} \\\\ \mathsf{(x + y)(2x + 2)} \\\\ \boxed{\mathsf{2(x + y)(x + 1)}}$

 Opção E)!!