Algebra Examples

$27 x^{3} - 125$

Step 1

Rewrite $27 x^{3}$ as ${(3 x)}^{3}$ .

${(3 x)}^{3} - 125$

Step 2

Rewrite $125$ as $5^{3}$ .

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

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 $a = 3 x$ and $b = 5$ .

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

Step 4

Simplify.

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Step 4.1

Apply the product rule to $3 x$ .

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

Step 4.2

Raise $3$ to the power of $2$ .

$(3 x - 5) (9 x^{2} + 3 x \cdot 5 + 5^{2})$

Step 4.3

Multiply $5$ by $3$ .

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

Step 4.4

Raise $5$ to the power of $2$ .

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