Factor completely.
-$$25 x ^ { 2 } - 20 x + 4 y ^ { 2 }$$
A) $( 2 x - 5 y ) ^ { 2 }$
B) $( 2 x + 5 y ) ^ { 2 }$
C) Prime
D) $( 5 x - y ) ^ { 2 }$

Question

Quizplus · Accepted Answer

We can see that the first two terms are perfect squares, specifically $(5x)^2$ and $(2y)^2$, and the last term is a perfect square, specifically $(2y)^2$. Also, the numerical coefficient of the perfect square $25$ and the factor of $4$ are both perfect squares, specifically $5^2$ and $2^2$, respectively. Therefore, we can write the expression as $$(5x)^2-2(5x)(2y)+(2y)^2=(5x-2y)^2$$ which is choice A.

Factor Completely 25x2−20x+4y225 x ^ { 2 } - 20 x + 4 y ^ { 2 }25x2−20x+4y2

Factor Completely $25 x ^ { 2 } - 20 x + 4 y ^ { 2 }$