Basic Math Examples

$2 a^{3} - 250 p^{9}$

Step 1

Factor $2$ out of $2 a^{3} - 250 p^{9}$ .

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Step 1.1

Factor $2$ out of $2 a^{3}$ .

$2 (a^{3}) - 250 p^{9}$

Step 1.2

Factor $2$ out of $- 250 p^{9}$ .

$2 (a^{3}) + 2 (- 125 p^{9})$

Step 1.3

Factor $2$ out of $2 (a^{3}) + 2 (- 125 p^{9})$ .

$2 (a^{3} - 125 p^{9})$

Step 2

Rewrite $125 p^{9}$ as ${(5 p^{3})}^{3}$ .

$2 (a^{3} - {(5 p^{3})}^{3})$

Step 3

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 $a = a$ and $b = 5 p^{3}$ .

$2 ((a - (5 p^{3})) (a^{2} + a (5 p^{3}) + {(5 p^{3})}^{2}))$

Step 4

Factor.

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Step 4.1

Simplify.

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Step 4.1.1

Multiply $5$ by $- 1$ .

$2 ((a - 5 p^{3}) (a^{2} + a (5 p^{3}) + {(5 p^{3})}^{2}))$

Step 4.1.2

Rewrite using the commutative property of multiplication.

$2 ((a - 5 p^{3}) (a^{2} + 5 a p^{3} + {(5 p^{3})}^{2}))$

Step 4.1.3

Apply the product rule to $5 p^{3}$ .

$2 ((a - 5 p^{3}) (a^{2} + 5 a p^{3} + 5^{2} {(p^{3})}^{2}))$

Step 4.1.4

Raise $5$ to the power of $2$ .

$2 ((a - 5 p^{3}) (a^{2} + 5 a p^{3} + 25 {(p^{3})}^{2}))$

Step 4.1.5

Multiply the exponents in ${(p^{3})}^{2}$ .

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Step 4.1.5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 ((a - 5 p^{3}) (a^{2} + 5 a p^{3} + 25 p^{3 \cdot 2}))$

Step 4.1.5.2

Multiply $3$ by $2$ .

$2 ((a - 5 p^{3}) (a^{2} + 5 a p^{3} + 25 p^{6}))$

Step 4.2

Remove unnecessary parentheses.

$2 (a - 5 p^{3}) (a^{2} + 5 a p^{3} + 25 p^{6})$