Algebra Examples

$81 x^{6} + 24 x^{3} y^{3}$

Step 1

Factor $3 x^{3}$ out of $81 x^{6} + 24 x^{3} y^{3}$ .

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Step 1.1

Factor $3 x^{3}$ out of $81 x^{6}$ .

$3 x^{3} (27 x^{3}) + 24 x^{3} y^{3}$

Step 1.2

Factor $3 x^{3}$ out of $24 x^{3} y^{3}$ .

$3 x^{3} (27 x^{3}) + 3 x^{3} (8 y^{3})$

Step 1.3

Factor $3 x^{3}$ out of $3 x^{3} (27 x^{3}) + 3 x^{3} (8 y^{3})$ .

$3 x^{3} (27 x^{3} + 8 y^{3})$

Step 2

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

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

Step 3

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

$3 x^{3} ({(3 x)}^{3} + {(2 y)}^{3})$

Step 4

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 $a = 3 x$ and $b = 2 y$ .

$3 x^{3} ((3 x + 2 y) ({(3 x)}^{2} - (3 x) (2 y) + {(2 y)}^{2}))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Apply the product rule to $3 x$ .

$3 x^{3} ((3 x + 2 y) (3^{2} x^{2} - (3 x) (2 y) + {(2 y)}^{2}))$

Step 5.1.2

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

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

Step 5.1.3

Multiply $3$ by $- 1$ .

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

Step 5.1.4

Rewrite using the commutative property of multiplication.

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

Step 5.1.5

Multiply $- 3$ by $2$ .

$3 x^{3} ((3 x + 2 y) (9 x^{2} - 6 x y + {(2 y)}^{2}))$

Step 5.1.6

Apply the product rule to $2 y$ .

$3 x^{3} ((3 x + 2 y) (9 x^{2} - 6 x y + 2^{2} y^{2}))$

Step 5.1.7

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

$3 x^{3} ((3 x + 2 y) (9 x^{2} - 6 x y + 4 y^{2}))$

Step 5.2

Remove unnecessary parentheses.

$3 x^{3} (3 x + 2 y) (9 x^{2} - 6 x y + 4 y^{2})$