Factor the expression. $$y ^ { 3 } + 64$$
A) $( y + 4 ) ^ { 3 }$
B) $( y - 4 ) \left( y ^ { 2 } + 4 y - 16 \right)$
C) $( y + 4 ) \left( y ^ { 2 } - 4 y + 16 \right)$
D) $( y - 4 ) \left( y ^ { 2 } - 4 y - 16 \right)$
E) $( y - 4 ) ^ { 3 }$

Question

Quizplus · Accepted Answer

This expression follows the sum of cubes formula which states that $a^3+b^3=(a+b)(a^2-ab+b^2)$. In this case, $a=y$ and $b=4$, so we have:
$$y^3+64=(y+4)(y^2-4y+16)$$
Option C matches this factorization.

Factor the Expression y3+64y ^ { 3 } + 64y3+64 A) (y+4)3( y + 4 ) ^ { 3 }(y+4)3

Factor the Expression $y ^ { 3 } + 64$ A) $( y + 4 ) ^ { 3 }$