Question

1. factor $25a^{4}-b^{4}$:

a. $(5a^{2}-b^{2})^{2}$
b. $(5a^{2}+b^{2})(5a^{2}-b^{2})$
c. $(5a^{2}+3b^{2})(5a^{2}-3b^{2})$
d. $(-5a^{2}+b^{2})(5a^{2}-b^{2})$

Explanation:

Step1: Recognize difference of squares

$25a^4 - b^4 = (5a^2)^2 - (b^2)^2$

Step2: Apply difference of squares formula

$\text{Use } x^2 - y^2=(x+y)(x-y), \text{ let } x=5a^2, y=b^2$
$25a^4 - b^4=(5a^2+b^2)(5a^2-b^2)$

Answer:

b. $(5a^{2}+b^{2})(5a^{2}-b^{2})$