Algebra Examples

$375 x^{3} - 24 y^{3}$

Step 1

Factor

$3$ out of

$375 x^{3} - 24 y^{3}$ .

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Step 1.1

Factor

$3$ out of

$375 x^{3}$ .

$3 (125 x^{3}) - 24 y^{3}$

Step 1.2

Factor

$3$ out of

$- 24 y^{3}$ .

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

Step 1.3

Factor

$3$ out of

$3 (125 x^{3}) + 3 (- 8 y^{3})$ .

$3 (125 x^{3} - 8 y^{3})$

Step 2

Rewrite

$125 x^{3}$ as

${(5 x)}^{3}$ .

$3 ({(5 x)}^{3} - 8 y^{3})$

Step 3

Rewrite

$8 y^{3}$ as

${(2 y)}^{3}$ .

$3 ({(5 x)}^{3} - {(2 y)}^{3})$

Step 4

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

$b = 2 y$ .

$3 ((5 x - (2 y)) ({(5 x)}^{2} + 5 x (2 y) + {(2 y)}^{2}))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Multiply

$2$ by

$- 1$ .

$3 ((5 x - 2 y) ({(5 x)}^{2} + 5 x (2 y) + {(2 y)}^{2}))$

Step 5.1.2

Apply the product rule to

$5 x$ .

$3 ((5 x - 2 y) (5^{2} x^{2} + 5 x (2 y) + {(2 y)}^{2}))$

Step 5.1.3

Raise

$5$ to the power of

$2$ .

$3 ((5 x - 2 y) (25 x^{2} + 5 x (2 y) + {(2 y)}^{2}))$

Step 5.1.4

Rewrite using the commutative property of multiplication.

$3 ((5 x - 2 y) (25 x^{2} + 5 \cdot 2 x y + {(2 y)}^{2}))$

Step 5.1.5

Multiply

$5$ by

$2$ .

$3 ((5 x - 2 y) (25 x^{2} + 10 x y + {(2 y)}^{2}))$

Step 5.1.6

Apply the product rule to

$2 y$ .

$3 ((5 x - 2 y) (25 x^{2} + 10 x y + 2^{2} y^{2}))$

Step 5.1.7

Raise

$2$ to the power of

$2$ .

$3 ((5 x - 2 y) (25 x^{2} + 10 x y + 4 y^{2}))$

Step 5.2

Remove unnecessary parentheses.

$3 (5 x - 2 y) (25 x^{2} + 10 x y + 4 y^{2})$