Factor completely. If the polynomial cannot be factored, write "prime."
-$216 y^{3}-343$
A) $(216 y-7)\left(y^{2}+42 y+49\right)$
B) $(6 y+7)\left(36 y^{2}-42 y+49\right)$
C) $(6 y-7)\left(36 y^{2}+49\right)$
D) $(6 y-7)\left(36 y^{2}+42 y+49\right)$

Question

Quizplus · Accepted Answer

The given polynomial is a difference of cubes: $216y^3 - 343 = (6y)^3 - 7^3$, which factors as $(a - b)(a^2 + ab + b^2)$, where $a = 6y$ and $b = 7$. This gives $(6y - 7)(36y^2 + 42y + 49)$.

Factor Completely 216y3−343216 y^{3}-343216y3−343 A) (216y−7)(y2+42y+49)(216 y-7)\left(y^{2}+42 y+49\right)(216y−7)(y2+42y+49) B) (6y+7)(36y2−42y+49)(6 y+7)\left(36 y^{2}-42 y+49\right)(6y+7)(36y2−42y+49)

Factor Completely $216 y^{3}-343$ A) $(216 y-7)\left(y^{2}+42 y+49\right)$ B) $(6 y+7)\left(36 y^{2}-42 y+49\right)$