Basic Math Examples

$\frac{a^{2} - y^{2}}{7 y - 7 a}$

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 $b = y$ .

$\frac{(a + y) (a - y)}{7 y - 7 a}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Factor $7$ out of $7 y - 7 a$ .

Tap for more steps...

Step 2.1.1

Factor $7$ out of $7 y$ .

$\frac{(a + y) (a - y)}{7 (y) - 7 a}$

Step 2.1.2

Factor $7$ out of $- 7 a$ .

$\frac{(a + y) (a - y)}{7 (y) + 7 (- a)}$

Step 2.1.3

Factor $7$ out of $7 (y) + 7 (- a)$ .

$\frac{(a + y) (a - y)}{7 (y - a)}$

Step 2.2

Cancel the common factor of $a - y$ and $y - a$ .

Tap for more steps...

Step 2.2.1

Factor $- 1$ out of $a$ .

$\frac{(a + y) (- 1 (- a) - y)}{7 (y - a)}$

Step 2.2.2

Factor $- 1$ out of $- y$ .

$\frac{(a + y) (- 1 (- a) - (y))}{7 (y - a)}$

Step 2.2.3

Factor $- 1$ out of $- 1 (- a) - (y)$ .

$\frac{(a + y) (- 1 (- a + y))}{7 (y - a)}$

Step 2.2.4

Reorder terms.

$\frac{(a + y) (- 1 (- a + y))}{7 (- a + y)}$

Step 2.2.5

Cancel the common factor.

$\frac{(a + y) (- 1 (- a + y))}{7 (- a + y)}$

Step 2.2.6

Rewrite the expression.

$\frac{(a + y) \cdot (- 1)}{7}$

Step 2.3

Simplify the expression.

Tap for more steps...

Step 2.3.1

Move $- 1$ to the left of $a + y$ .

$\frac{- 1 \cdot (a + y)}{7}$

Step 2.3.2

Move the negative in front of the fraction.

$- \frac{a + y}{7}$