Pre-Algebra Examples

$40 - 5 x^{3}$

Step 1

Factor $5$ out of $40 - 5 x^{3}$ .

Tap for more steps...

Step 1.1

Factor $5$ out of $40$ .

$5 (8) - 5 x^{3}$

Step 1.2

Factor $5$ out of $- 5 x^{3}$ .

$5 (8) + 5 (- x^{3})$

Step 1.3

Factor $5$ out of $5 (8) + 5 (- x^{3})$ .

$5 (8 - x^{3})$

Step 2

Rewrite $8$ as $2^{3}$ .

$5 (2^{3} - x^{3})$

Step 3

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

$5 ((2 - x) (2^{2} + 2 x + x^{2}))$

Step 4

Factor.

Tap for more steps...

Step 4.1

Raise $2$ to the power of $2$ .

$5 ((2 - x) (4 + 2 x + x^{2}))$

Step 4.2

Remove unnecessary parentheses.

$5 (2 - x) (4 + 2 x + x^{2})$