Factor: $64 x ^ { 2 } - 25$
A) $( 5 + 8 x ) ( 5 - 8 x )$
B) $( 8 x - 5 ) ^ { 2 }$
C) $( 8 x + 5 ) ^ { 2 }$
D) $( 8 x + 5 ) ( 8 x - 5 )$
E) Nonfactorable over the integers

Question

Quizplus · Accepted Answer

This expression is a difference of squares, with $64 x ^ { 2 }$ being the perfect square of $8 x$ and 25 being the perfect square of 5. Therefore, we can use the formula $a^2-b^2 = (a+b)(a-b)$ and factor the expression as $(8 x + 5)(8 x - 5)$. Option D is the only choice that matches this factorization.

Factor 64x2−2564 x ^ { 2 } - 2564x2−25 A) (5+8x)(5−8x)( 5 + 8 x ) ( 5 - 8 x )(5+8x)(5−8x)

Factor $64 x ^ { 2 } - 25$ A) $( 5 + 8 x ) ( 5 - 8 x )$