Algebra Examples

$p^{3} + 125 q^{3}$

Step 1

Rewrite

$125 q^{3}$ as

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

$p^{3} + {(5 q)}^{3}$

Step 2

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

$a = p$ and

$b = 5 q$ .

$(p + 5 q) (p^{2} - p (5 q) + {(5 q)}^{2})$

Step 3

Simplify.

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Step 3.1

Rewrite using the commutative property of multiplication.

$(p + 5 q) (p^{2} - 1 \cdot 5 p q + {(5 q)}^{2})$

Step 3.2

Multiply

$- 1$ by

$5$ .

$(p + 5 q) (p^{2} - 5 p q + {(5 q)}^{2})$

Step 3.3

Apply the product rule to

$5 q$ .

$(p + 5 q) (p^{2} - 5 p q + 5^{2} q^{2})$

Step 3.4

Raise

$5$ to the power of

$2$ .

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