Trigonometry Examples

$5 x^{3} + 40 z^{3}$

Step 1

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

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Step 1.1

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

$5 (x^{3}) + 40 z^{3}$

Step 1.2

Factor $5$ out of $40 z^{3}$ .

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

Step 1.3

Factor $5$ out of $5 (x^{3}) + 5 (8 z^{3})$ .

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

Step 2

Rewrite $8 z^{3}$ as ${(2 z)}^{3}$ .

$5 (x^{3} + {(2 z)}^{3})$

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 $b = 2 z$ .

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

Step 4

Factor.

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Step 4.1

Simplify.

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Step 4.1.1

Rewrite using the commutative property of multiplication.

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

Step 4.1.2

Multiply $- 1$ by $2$ .

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

Step 4.1.3

Apply the product rule to $2 z$ .

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

Step 4.1.4

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

$5 ((x + 2 z) (x^{2} - 2 x z + 4 z^{2}))$

Step 4.2

Remove unnecessary parentheses.

$5 (x + 2 z) (x^{2} - 2 x z + 4 z^{2})$