Basic Math Examples

$\frac{a y - 3 y}{a - y} \cdot \frac{a^{2} - y^{2}}{y}$

Step 1

Factor $y$ out of $a y - 3 y$ .

Tap for more steps...

Step 1.1

Factor $y$ out of $a y$ .

$\frac{y a - 3 y}{a - y} \cdot \frac{a^{2} - y^{2}}{y}$

Step 1.2

Factor $y$ out of $- 3 y$ .

$\frac{y a + y \cdot - 3}{a - y} \cdot \frac{a^{2} - y^{2}}{y}$

Step 1.3

Factor $y$ out of $y a + y \cdot - 3$ .

$\frac{y (a - 3)}{a - y} \cdot \frac{a^{2} - y^{2}}{y}$

Step 2

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 $b = y$ .

$\frac{y (a - 3)}{a - y} \cdot \frac{(a + y) (a - y)}{y}$

Step 3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1

Cancel the common factor of $y$ .

Tap for more steps...

Step 3.1.1

Cancel the common factor.

$\frac{y (a - 3)}{a - y} \cdot \frac{(a + y) (a - y)}{y}$

Step 3.1.2

Rewrite the expression.

$\frac{a - 3}{a - y} \cdot ((a + y) (a - y))$

Step 3.2

Cancel the common factor of $a - y$ .

Tap for more steps...

Step 3.2.1

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

$\frac{a - 3}{a - y} \cdot ((a - y) (a + y))$

Step 3.2.2

Cancel the common factor.

$\frac{a - 3}{a - y} \cdot ((a - y) (a + y))$

Step 3.2.3

Rewrite the expression.

$(a - 3) \cdot (a + y)$

Step 4

Expand $(a - 3) (a + y)$ using the FOIL Method.

Tap for more steps...

Step 4.1

Apply the distributive property.

$a (a + y) - 3 (a + y)$

Step 4.2

Apply the distributive property.

$a \cdot a + a y - 3 (a + y)$

Step 4.3

Apply the distributive property.

$a \cdot a + a y - 3 a - 3 y$

Step 5

Simplify the expression.

Tap for more steps...

Step 5.1

Multiply $a$ by $a$ .

$a^{2} + a y - 3 a - 3 y$

Step 5.2

Move $- 3 a$ .

$a^{2} + a y - 3 y - 3 a$

Step 5.3

Reorder $a^{2}$ and $a y$ .

$a y + a^{2} - 3 y - 3 a$