Algebra Examples

$125 x^{3} - 27$

Step 1

Rewrite

$125 x^{3}$ as

${(5 x)}^{3}$ .

${(5 x)}^{3} - 27$

Step 2

Rewrite

$27$ as

$3^{3}$ .

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

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

$a = 5 x$ and

$b = 3$ .

$(5 x - 3) ({(5 x)}^{2} + 5 x \cdot 3 + 3^{2})$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Apply the product rule to

$5 x$ .

$(5 x - 3) (5^{2} x^{2} + 5 x \cdot 3 + 3^{2})$

Step 4.2

Raise

$5$ to the power of

$2$ .

$(5 x - 3) (25 x^{2} + 5 x \cdot 3 + 3^{2})$

Step 4.3

Multiply

$3$ by

$5$ .

$(5 x - 3) (25 x^{2} + 15 x + 3^{2})$

Step 4.4

Raise

$3$ to the power of

$2$ .

$(5 x - 3) (25 x^{2} + 15 x + 9)$