select the correct answer.\nwhat is the factored form of $x^{3}+216$?\na. $(x - 6)(x^{2}+6x + 36)$\nb. $(x +…

select the correct answer.\nwhat is the factored form of $x^{3}+216$?\na. $(x - 6)(x^{2}+6x + 36)$\nb. $(x + 6)(x^{2}-6x + 36)$\nc. $(x + 6)(x^{2}-12x + 36)$\nd. $(x + 6)(x^{2}+12x + 36)$

select the correct answer.\nwhat is the factored form of $x^{3}+216$?\na. $(x - 6)(x^{2}+6x + 36)$\nb. $(x + 6)(x^{2}-6x + 36)$\nc. $(x + 6)(x^{2}-12x + 36)$\nd. $(x + 6)(x^{2}+12x + 36)$

Answer

Explanation:

Step1: Recall sum - of - cubes formula

The sum - of - cubes formula is $a^{3}+b^{3}=(a + b)(a^{2}-ab + b^{2})$. In the expression $x^{3}+216$, we know that $x^{3}=x^{3}$ and $216 = 6^{3}$, so $a=x$ and $b = 6$.

Step2: Apply the formula

Substitute $a=x$ and $b = 6$ into the sum - of - cubes formula: $x^{3}+6^{3}=(x + 6)(x^{2}-6x+36)$

Answer:

B. $(x + 6)(x^{2}-6x + 36)$