Basic Math Examples

$a^{3} + 3 a^{2} - 9 a - 27$

Step 1

Factor out the greatest common factor from each group.

Tap for more steps...

Step 1.1

Group the first two terms and the last two terms.

$(a^{3} + 3 a^{2}) - 9 a - 27$

Step 1.2

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

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

Step 2

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

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

Step 3

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

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

Step 4

Factor.

Tap for more steps...

Step 4.1

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 $b = 3$ .

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

Step 4.2

Remove unnecessary parentheses.

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

Step 5

Combine exponents.

Tap for more steps...

Step 5.1

Raise $a + 3$ to the power of $1$ .

${(a + 3)}^{1} (a + 3) (a - 3)$

Step 5.2

Raise $a + 3$ to the power of $1$ .

${(a + 3)}^{1} {(a + 3)}^{1} (a - 3)$

Step 5.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(a + 3)}^{1 + 1} (a - 3)$

Step 5.4

Add $1$ and $1$ .

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