Question

factor $25x^{2}-16y^{2}$:
a. not factorable
b. $(5x - 4y)^{2}$
c. $(5x + 4y)(5x - 4y)$
d. $(5x + 4y)(5x + 4y)$

Explanation:

Step1: Recognize difference of squares

$25x^2 - 16y^2 = (5x)^2 - (4y)^2$

Step2: Apply difference of squares formula

$a^2 - b^2 = (a+b)(a-b)$, so substitute $a=5x$, $b=4y$:
$(5x)^2 - (4y)^2 = (5x + 4y)(5x - 4y)$

Answer:

c. $(5x + 4y)(5x - 4y)$