Factor the expression completely. If the expression is prime, so indicate. $64 x ^ { 4 } - 64$
A) $64 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } - 1 \right)$
B) $\left( 8 x ^ { 2 } - 8 \right) ( x + 1 ) ( 8 x - 8 )$
C) $64 \left( x ^ { 2 } + 1 \right) ( x + 1 ) ( x - 1 )$
D) $8 \left( 8 x ^ { 2 } - 1 \right) ( x + 1 ) ( x - 8 )$
E) prime

Question

Quizplus · Accepted Answer

We can begin by factoring out the greatest common factor of 64 to get $$64(x^4-1).$$ Notice that we have a difference of squares inside the parentheses, so we can factor that as well: $$64(x^2+1)(x^2-1).$$ Finally, we can factor the expression $x^2-1$ as a difference of squares to get the fully factored expression: $$64(x^2+1)(x+1)(x-1).$$

Factor the Expression Completely 64x4−6464 x ^ { 4 } - 6464x4−64

Factor the Expression Completely $64 x ^ { 4 } - 64$