Question

factor $25x^{4}-4y^{4}$:
a. $(x^{2}+2y^{2})(x^{2}-2y^{2})$
b. $(25x^{2}+4y^{2})^{2}$
c. $(5x^{2}-2y)^{2}$
d. $(5x^{2}+2y^{2})(5x^{2}-2y^{2})$

Explanation:

Step1: Recognize difference of squares

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

Step2: Apply difference of squares formula

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

Answer:

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