Question

1. factor $64r^{4}-36$:a. $16(4r^{2}+3)(4r^{2}-3)$b. $16(r^{2}-3)^{2}$c. $4(4r^{2}+3)(4r^{2}-3)$d. $4(r^{2}+5)(r^{2}-5)$

Explanation:

Step1: Factor out GCF

Identify greatest common factor (GCF) of $64r^4$ and $36$, which is $4$.
$64r^4 - 36 = 4(16r^4 - 9)$

Step2: Recognize difference of squares

Rewrite $16r^4 -9$ as $(4r^2)^2 - 3^2$, a difference of squares $a^2-b^2=(a+b)(a-b)$.
$16r^4 - 9 = (4r^2 + 3)(4r^2 - 3)$

Step3: Combine factors

Substitute back into the expression from Step1.
$64r^4 - 36 = 4(4r^2+3)(4r^2-3)$

Answer:

c. $4(4r^{2}+3)(4r^{2}-3)$