Factor 5k^3+40

$5 k^{3} + 40$

Step 1

Factor $5$ out of $5 k^{3} + 40$ .

Factor $5$ out of $5 k^{3}$ .

$5 (k^{3}) + 40$

Factor $5$ out of $40$ .

$5 k^{3} + 5 \cdot 8$

Factor $5$ out of $5 k^{3} + 5 \cdot 8$ .

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

Step 2

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

$5 (k^{3} + 2^{3})$

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 $a = k$ and $b = 2$ .

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

Step 4

Factor.

Simplify.

Multiply $2$ by $- 1$ .

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

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

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

Remove unnecessary parentheses.

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

Factor 5k^3+40

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