Factor the polynomial completely. Don t forget to look for a common monomial factor first. $2 x ^ { 2 } - 32 y ^ { 2 }$
A) $2 ( x - 4 y ) ( x + 4 y )$
B) $4 ( x - 2 y ) ( x + 2 y )$
C) $( x - 2 y ) ( x + 2 y )$
D) $( x - 4 y ) ( x + 4 y )$
E) not factorable

Question

Quizplus · Accepted Answer

This polynomial is a difference of squares, which can be factored as $a^2 - b^2 = (a - b)(a + b)$. Here, $a^2 = (2x)^2 = 4x^2$ and $b^2 = (4y)^2 = 16y^2$, so the polynomial $2x^2 - 32y^2$ can be factored as $2(x^2 - 16y^2) = 2(x^2 - (4y)^2) = 2(x - 4y)(x + 4y)$.

Factor the Polynomial Completely 2x2−32y22 x ^ { 2 } - 32 y ^ { 2 }2x2−32y2

Factor the Polynomial Completely $2 x ^ { 2 } - 32 y ^ { 2 }$