Factor.
-$27 \mathrm{c}^{3}+1000$
A) $(3 c+10)\left(9 c^{2}+100\right)$
B) $(27 c+10)\left(c^{2}-30 c+100\right)$
C) $(3 c+10)\left(9 c^{2}-30 c+100\right)$
D) $(3 c-10)\left(9 c^{2}+30 c+100\right)$

Question

Quizplus · Accepted Answer

This is a sum of cubes factorization, where $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$. Here, $27c^3 = (3c)^3$ and $1000 = 10^3$, so the factorization is $(3c + 10)((3c)^2 - 3c*10 + 10^2)$, which simplifies to $(3c + 10)(9c^2 - 30c + 100)$.

Factor - 27c3+100027 \mathrm{c}^{3}+100027c3+1000 A) (3c+10)(9c2+100)(3 c+10)\left(9 c^{2}+100\right)(3c+10)(9c2+100) B) (27c+10)(c2−30c+100)(27 c+10)\left(c^{2}-30 c+100\right)(27c+10)(c2−30c+100) C) (3c+10)(9c2−30c+100)(3 c+10)\left(9 c^{2}-30 c+100\right)(3c+10)(9c2−30c+100)

Factor
- $27 \mathrm{c}^{3}+1000$ A) $(3 c+10)\left(9 c^{2}+100\right)$ B) $(27 c+10)\left(c^{2}-30 c+100\right)$ C) $(3 c+10)\left(9 c^{2}-30 c+100\right)$