Question

1. factor (25x^4 - 9y^4).

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

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 $a=5x^2$, $b=3y^2$:
$(5x^2+3y^2)(5x^2-3y^2)$

Answer:

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