Basic Math Examples

$\frac{y^{2} + 6 y - 27}{2 y^{2} - 2 y - 144}$

Step 1

Factor $y^{2} + 6 y - 27$ using the AC method.

Tap for more steps...

Step 1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 27$ and whose sum is $6$ .

$- 3, 9$

Step 1.2

Write the factored form using these integers.

$\frac{(y - 3) (y + 9)}{2 y^{2} - 2 y - 144}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Factor $2$ out of $2 y^{2} - 2 y - 144$ .

Tap for more steps...

Step 2.1.1

Factor $2$ out of $2 y^{2}$ .

$\frac{(y - 3) (y + 9)}{2 (y^{2}) - 2 y - 144}$

Step 2.1.2

Factor $2$ out of $- 2 y$ .

$\frac{(y - 3) (y + 9)}{2 (y^{2}) + 2 (- y) - 144}$

Step 2.1.3

Factor $2$ out of $- 144$ .

$\frac{(y - 3) (y + 9)}{2 (y^{2}) + 2 (- y) + 2 (- 72)}$

Step 2.1.4

Factor $2$ out of $2 (y^{2}) + 2 (- y)$ .

$\frac{(y - 3) (y + 9)}{2 (y^{2} - y) + 2 (- 72)}$

Step 2.1.5

Factor $2$ out of $2 (y^{2} - y) + 2 (- 72)$ .

$\frac{(y - 3) (y + 9)}{2 (y^{2} - y - 72)}$

Step 2.2

Factor $y^{2} - y - 72$ using the AC method.

Tap for more steps...

Step 2.2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 72$ and whose sum is $- 1$ .

$- 9, 8$

Step 2.2.2

Write the factored form using these integers.

$\frac{(y - 3) (y + 9)}{2 ((y - 9) (y + 8))}$

$\frac{(y - 3) (y + 9)}{2 (y - 9) (y + 8)}$