Pre-Algebra Examples

$(16 x^{2} - 25) \div (4 x + 5)$

Step 1

Rewrite the division as a fraction.

$\frac{16 x^{2} - 25}{4 x + 5}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

$\frac{{(4 x)}^{2} - 25}{4 x + 5}$

Step 2.2

Rewrite $25$ as $5^{2}$ .

$\frac{{(4 x)}^{2} - 5^{2}}{4 x + 5}$

Step 2.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 x$ and $b = 5$ .

$\frac{(4 x + 5) (4 x - 5)}{4 x + 5}$

Step 3

Cancel the common factor of $4 x + 5$ .

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Step 3.1

Cancel the common factor.

$\frac{(4 x + 5) (4 x - 5)}{4 x + 5}$

Step 3.2

Divide $4 x - 5$ by $1$ .

$4 x - 5$