Factor 8x^3+1000

$8 x^{3} + 1000$

Step 1

Factor $8$ out of $8 x^{3} + 1000$ .

Factor $8$ out of $8 x^{3}$ .

$8 (x^{3}) + 1000$

Factor $8$ out of $1000$ .

$8 x^{3} + 8 \cdot 125$

Factor $8$ out of $8 x^{3} + 8 \cdot 125$ .

$8 (x^{3} + 125)$

Step 2

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

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

Step 3

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = x$ and $b = 5$ .

$8 ((x + 5) (x^{2} - x \cdot 5 + 5^{2}))$

Step 4

Factor.

Simplify.

Multiply $5$ by $- 1$ .

$8 ((x + 5) (x^{2} - 5 x + 5^{2}))$

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

$8 ((x + 5) (x^{2} - 5 x + 25))$

Remove unnecessary parentheses.

$8 (x + 5) (x^{2} - 5 x + 25)$

Factor 8x^3+1000

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