Factor by Grouping 18-2a^2-27a+3a^3

$18 - 2 a^{2} - 27 a + 3 a^{3}$

Step 1

Reorder terms.

$3 a^{3} - 2 a^{2} - 27 a + 18$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 a^{3} - 2 a^{2}) - 27 a + 18$

Factor out the greatest common factor (GCF) from each group.

$a^{2} (3 a - 2) - 9 (3 a - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 a - 2$ .

$(3 a - 2) (a^{2} - 9)$

Step 4

Rewrite $9$ as $3^{2}$ .

$(3 a - 2) (a^{2} - 3^{2})$

Step 5

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = 3$ .

$(3 a - 2) ((a + 3) (a - 3))$

Remove unnecessary parentheses.

$(3 a - 2) (a + 3) (a - 3)$