Question

factor $4u^4 - 16v^4$:
a. $4(u^2 + 2v^2)(u^2 - 2v^2)$
b. $16(u^2 - 2v^2)^2$
c. $(u^2 + 2v^2)^2$
d. $4(5u^2 + v^2)(5u^2 - v^2)$

Explanation:

Step1: Factor out GCF

Factor out 4 from the expression:
$4u^4 - 16v^4 = 4(u^4 - 4v^4)$

Step2: Recognize difference of squares

Rewrite $u^4 - 4v^4$ as $(u^2)^2 - (2v^2)^2$, then apply $a^2-b^2=(a+b)(a-b)$:
$4[(u^2)^2 - (2v^2)^2] = 4(u^2+2v^2)(u^2-2v^2)$

Answer:

a. $4(u^{2}+2v^{2})(u^{2}-2v^{2})$