3. Factor the expression a^3+216 A. (a+6)(a^2+6a+18) B. (a+6)(a^2-6a+18) C. (a+6)(a^2-6a+36) D. (a-6)(a^2+6a+36)

To factor the expression $a^{3}+216$, we can use the sum of cubes formula, which states that $a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})$.<br /><br />In this case, we have $a^{3}+216$, which can be rewritten as $a^{3}+6^{3}$. Applying the sum of cubes formula, we get:<br /><br />$a^{3}+6^{3}=(a+6)(a^{2}-6a+36)$<br /><br />Therefore, the correct answer is C. $(a+6)(a^{2}-6a+36)$.