Basic Math Examples

$125 a^{3} + b^{3}$

Step 1

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

${(5 a)}^{3} + b^{3}$

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 $a = 5 a$ and $b = b$ .

$(5 a + b) ({(5 a)}^{2} - (5 a) b + b^{2})$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Apply the product rule to $5 a$ .

$(5 a + b) (5^{2} a^{2} - (5 a) b + b^{2})$

Step 3.2

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

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

Step 3.3

Multiply $5$ by $- 1$ .

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