Question

1. factor ( 64r^4 - 36 ):

a. ( 16(4r^2 + 3)(4r^2 - 3) )
b. ( 4(r^2 + 5)(r^2 - 5) )
c. ( 4(4r^2 + 3)(4r^2 - 3) )
d. ( 16(r^2 - 3)^2 )

Explanation:

Step1: Factor out GCF

Factor 4 from the expression:
$64r^4 - 36 = 4(16r^4 - 9)$

Step2: Recognize difference of squares

Rewrite $16r^4 -9$ as $(4r^2)^2 - 3^2$, then apply $a^2-b^2=(a+b)(a-b)$:
$16r^4 -9=(4r^2+3)(4r^2-3)$

Step3: Combine factors

Substitute back into the expression:
$64r^4 - 36=4(4r^{2}+3)(4r^{2}-3)$

Answer:

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