Factor the polynomial completely
-$x^{2}-y^{2}+8 y-16$
A) $(1-4)(x+y)(x-y)$
B) $(x+y-4)(x-y-4)$
C) $(\mathrm{x}-\mathrm{y}-4)(\mathrm{x}-\mathrm{y}+4)$
D) $(x+y-4)(x-y+4)$

Question

Quizplus · Accepted Answer

The polynomial can be rewritten as $x^2 - (y^2 - 8y + 16)$. Recognizing $y^2 - 8y + 16$ as a perfect square trinomial $(y-4)^2$, the expression becomes $x^2 - (y-4)^2$, which factors as a difference of squares: $(x + (y-4))(x - (y-4)) = (x+y-4)(x-y+4)$.