Basic Math Examples

24 b^{3} + 2187 p^{3}

$24 b^{3} + 2187 p^{3}$

Step 1

Factor

3

$3$ out of

24 b^{3} + 2187 p^{3}

$24 b^{3} + 2187 p^{3}$ .

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Step 1.1

Factor

3

$3$ out of

24 b^{3}

$24 b^{3}$ .

3 (8 b^{3}) + 2187 p^{3}

$3 (8 b^{3}) + 2187 p^{3}$

Step 1.2

Factor

3

$3$ out of

2187 p^{3}

$2187 p^{3}$ .

3 (8 b^{3}) + 3 (729 p^{3})

$3 (8 b^{3}) + 3 (729 p^{3})$

Step 1.3

Factor

3

$3$ out of

3 (8 b^{3}) + 3 (729 p^{3})

$3 (8 b^{3}) + 3 (729 p^{3})$ .

3 (8 b^{3} + 729 p^{3})

$3 (8 b^{3} + 729 p^{3})$

3 (8 b^{3} + 729 p^{3})

$3 (8 b^{3} + 729 p^{3})$

Step 2

Rewrite

8 b^{3}

$8 b^{3}$ as

{(2 b)}^{3}

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

3 ({(2 b)}^{3} + 729 p^{3})

$3 ({(2 b)}^{3} + 729 p^{3})$

Step 3

Rewrite

729 p^{3}

$729 p^{3}$ as

{(9 p)}^{3}

${(9 p)}^{3}$ .

3 ({(2 b)}^{3} + {(9 p)}^{3})

$3 ({(2 b)}^{3} + {(9 p)}^{3})$

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})

$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where

a = 2 b

$a = 2 b$ and

b = 9 p

$b = 9 p$ .

3 ((2 b + 9 p) ({(2 b)}^{2} - (2 b) (9 p) + {(9 p)}^{2}))

$3 ((2 b + 9 p) ({(2 b)}^{2} - (2 b) (9 p) + {(9 p)}^{2}))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Apply the product rule to

2 b

$2 b$ .

3 ((2 b + 9 p) (2^{2} b^{2} - (2 b) (9 p) + {(9 p)}^{2}))

$3 ((2 b + 9 p) (2^{2} b^{2} - (2 b) (9 p) + {(9 p)}^{2}))$

Step 5.1.2

Raise

2

$2$ to the power of

2

$2$ .

3 ((2 b + 9 p) (4 b^{2} - (2 b) (9 p) + {(9 p)}^{2}))

$3 ((2 b + 9 p) (4 b^{2} - (2 b) (9 p) + {(9 p)}^{2}))$

Step 5.1.3

Multiply

2

$2$ by

- 1

$- 1$ .

3 ((2 b + 9 p) (4 b^{2} - 2 b (9 p) + {(9 p)}^{2}))

$3 ((2 b + 9 p) (4 b^{2} - 2 b (9 p) + {(9 p)}^{2}))$

Step 5.1.4

Rewrite using the commutative property of multiplication.

3 ((2 b + 9 p) (4 b^{2} - 2 \cdot 9 b p + {(9 p)}^{2}))

$3 ((2 b + 9 p) (4 b^{2} - 2 \cdot 9 b p + {(9 p)}^{2}))$

Step 5.1.5

Multiply

- 2

$- 2$ by

9

$9$ .

3 ((2 b + 9 p) (4 b^{2} - 18 b p + {(9 p)}^{2}))

$3 ((2 b + 9 p) (4 b^{2} - 18 b p + {(9 p)}^{2}))$

Step 5.1.6

Apply the product rule to

9 p

$9 p$ .

3 ((2 b + 9 p) (4 b^{2} - 18 b p + 9^{2} p^{2}))

$3 ((2 b + 9 p) (4 b^{2} - 18 b p + 9^{2} p^{2}))$

Step 5.1.7

Raise

9

$9$ to the power of

2

$2$ .

3 ((2 b + 9 p) (4 b^{2} - 18 b p + 81 p^{2}))

$3 ((2 b + 9 p) (4 b^{2} - 18 b p + 81 p^{2}))$

3 ((2 b + 9 p) (4 b^{2} - 18 b p + 81 p^{2}))

$3 ((2 b + 9 p) (4 b^{2} - 18 b p + 81 p^{2}))$

Step 5.2

Remove unnecessary parentheses.

3 (2 b + 9 p) (4 b^{2} - 18 b p + 81 p^{2})

$3 (2 b + 9 p) (4 b^{2} - 18 b p + 81 p^{2})$

3 (2 b + 9 p) (4 b^{2} - 18 b p + 81 p^{2})

$3 (2 b + 9 p) (4 b^{2} - 18 b p + 81 p^{2})$