Simplify (5-80x^2)/10

$\frac{5 - 80 x^{2}}{10}$

Step 1

Cancel the common factor of $5 - 80 x^{2}$ and $10$ .

Factor $5$ out of $5$ .

$\frac{5 (1) - 80 x^{2}}{10}$

Factor $5$ out of $- 80 x^{2}$ .

$\frac{5 (1) + 5 (- 16 x^{2})}{10}$

Factor $5$ out of $5 (1) + 5 (- 16 x^{2})$ .

$\frac{5 (1 - 16 x^{2})}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

$\frac{5 (1 - 16 x^{2})}{5 \cdot 2}$

Cancel the common factor.

$\frac{5 (1 - 16 x^{2})}{5 \cdot 2}$

Rewrite the expression.

$\frac{1 - 16 x^{2}}{2}$

Step 2

Simplify the numerator.

Rewrite $1$ as $1^{2}$ .

$\frac{1^{2} - 16 x^{2}}{2}$

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

$\frac{1^{2} - {(4 x)}^{2}}{2}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = 4 x$ .

$\frac{(1 + 4 x) (1 - (4 x))}{2}$

Multiply $4$ by $- 1$ .

$\frac{(1 + 4 x) (1 - 4 x)}{2}$