Factor completely.
$a^{3} - 27$

Select the correct choice below and, if necessary,

Answer

Expert–verified

Hide Steps

Answer

So, the completely factored form of $a^{3} - 27$ is $(a - 3) (a^{2} + 3 a + 9)$

Steps

Step 1 ：Given expression is $a^{3} - 27$

Step 2 ：This is a difference of cubes, which can be factored using the formula $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$

Step 3 ：In this case, $a = a$ and $b = 3$

Step 4 ：Applying the formula, we get $a^{3} - 27 = a^{3} - 3^{3} = (a - 3) (a^{2} + 3 a + 9)$

Step 5 ：So, the completely factored form of $a^{3} - 27$ is $(a - 3) (a^{2} + 3 a + 9)$