Question

1. factor $25x^{4}-9y^{4}$:

a. $(2x^{2}+5y^{2})(2x^{2}-5y^{2})$
b. $(5x^{2}+3y^{2})(5x^{2}-3y^{2})$
c. $(25x^{2}+9y^{2})^{2}$
d. not factorable

Explanation:

Step1: Recognize difference of squares

$25x^4 - 9y^4 = (5x^2)^2 - (3y^2)^2$

Step2: Apply difference of squares formula

$a^2 - b^2 = (a+b)(a-b)$, so substitute $a=5x^2$, $b=3y^2$
$(5x^2)^2 - (3y^2)^2 = (5x^{2}+3y^{2})(5x^{2}-3y^{2})$

Answer:

b. $(5x^{2}+3y^{2})(5x^{2}-3y^{2})$