Question

factor $9x^4 - 4y^4$.
a. $(x^2 + 2y^2)(x^2 - 2y^2)$
b. $(9x^2 + 4y^2)^2$
c. $(2x^2 + y^2)(2x^2 - y^2)$
d. $(3x^2 + 2y^2)(3x^2 - 2y^2)$

Explanation:

Step1: Recognize difference of squares

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

Step2: Apply difference of squares formula

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

Answer:

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