Basic Math Examples

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

Step 1

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

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

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

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

Step 3

Simplify.

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Step 3.1

Rewrite using the commutative property of multiplication.

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

Step 3.2

Multiply $- 1$ by $5$ .

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

Step 3.3

Apply the product rule to $5 y$ .

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

Step 3.4

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

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