Basic Math Examples

$\sqrt{(a - b) (a^{2} - b^{2})}$

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = b$ .

$\sqrt{(a - b) (a + b) (a - b)}$

Step 2

Combine exponents.

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Step 2.1

Raise $a - b$ to the power of $1$ .

$\sqrt{{(a - b)}^{1} (a - b) (a + b)}$

Step 2.2

Raise $a - b$ to the power of $1$ .

$\sqrt{{(a - b)}^{1} {(a - b)}^{1} (a + b)}$

Step 2.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt{{(a - b)}^{1 + 1} (a + b)}$

Step 2.4

Add $1$ and $1$ .

$\sqrt{{(a - b)}^{2} (a + b)}$

Step 3

Pull terms out from under the radical.

$(a - b) \sqrt{a + b}$