Algebra Examples

$125 x^{3} - 1$

Step 1

Rewrite $125 x^{3}$ as ${(5 x)}^{3}$ .

${(5 x)}^{3} - 1$

Step 2

Rewrite $1$ as $1^{3}$ .

${(5 x)}^{3} - 1^{3}$

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 $b = 1$ .

$(5 x - 1) ({(5 x)}^{2} + 5 x \cdot 1 + 1^{2})$

Step 4

Simplify.

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Step 4.1

Apply the product rule to $5 x$ .

$(5 x - 1) (5^{2} x^{2} + 5 x \cdot 1 + 1^{2})$

Step 4.2

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

$(5 x - 1) (25 x^{2} + 5 x \cdot 1 + 1^{2})$

Step 4.3

Multiply $5$ by $1$ .

$(5 x - 1) (25 x^{2} + 5 x + 1^{2})$

Step 4.4

One to any power is one.

$(5 x - 1) (25 x^{2} + 5 x + 1)$