Precalculus Examples

$1 + 125 y^{3}$

Step 1

Rewrite $1$ as $1^{3}$ .

$1^{3} + 125 y^{3}$

Step 2

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

$1^{3} + {(5 y)}^{3}$

Step 3

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 $a = 1$ and $b = 5 y$ .

$(1 + 5 y) (1^{2} - 1 (5 y) + {(5 y)}^{2})$

Step 4

Simplify.

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Step 4.1

One to any power is one.

$(1 + 5 y) (1 - 1 (5 y) + {(5 y)}^{2})$

Step 4.2

Multiply $5$ by $- 1$ .

$(1 + 5 y) (1 - 5 y + {(5 y)}^{2})$

Step 4.3

Apply the product rule to $5 y$ .

$(1 + 5 y) (1 - 5 y + 5^{2} y^{2})$

Step 4.4

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

$(1 + 5 y) (1 - 5 y + 25 y^{2})$