Algebra Examples

$\frac{x^{3} + 8 x^{2}}{x^{2} + x - 56} \cdot \frac{x^{2} - 11 x + 28}{4 x}$

Step 1

Factor $x^{2}$ out of $x^{3} + 8 x^{2}$ .

Tap for more steps...

Step 1.1

Factor $x^{2}$ out of $x^{3}$ .

$\frac{x^{2} x + 8 x^{2}}{x^{2} + x - 56} \cdot \frac{x^{2} - 11 x + 28}{4 x}$

Step 1.2

Factor $x^{2}$ out of $8 x^{2}$ .

$\frac{x^{2} x + x^{2} \cdot 8}{x^{2} + x - 56} \cdot \frac{x^{2} - 11 x + 28}{4 x}$

Step 1.3

Factor $x^{2}$ out of $x^{2} x + x^{2} \cdot 8$ .

$\frac{x^{2} (x + 8)}{x^{2} + x - 56} \cdot \frac{x^{2} - 11 x + 28}{4 x}$

Step 2

Factor $x^{2} + x - 56$ using the AC method.

Tap for more steps...

Step 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 $- 56$ and whose sum is $1$ .

$- 7, 8$

Step 2.2

Write the factored form using these integers.

$\frac{x^{2} (x + 8)}{(x - 7) (x + 8)} \cdot \frac{x^{2} - 11 x + 28}{4 x}$

Step 3

Factor $x^{2} - 11 x + 28$ using the AC method.

Tap for more steps...

Step 3.1

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 $28$ and whose sum is $- 11$ .

$- 7, - 4$

Step 3.2

Write the factored form using these integers.

$\frac{x^{2} (x + 8)}{(x - 7) (x + 8)} \cdot \frac{(x - 7) (x - 4)}{4 x}$

Step 4

Simplify terms.

Tap for more steps...

Step 4.1

Combine.

$\frac{x^{2} (x + 8) ((x - 7) (x - 4))}{(x - 7) (x + 8) (4 x)}$

Step 4.2

Cancel the common factor of $x^{2}$ and $x$ .

Tap for more steps...

Step 4.2.1

Factor $x$ out of $x^{2} (x + 8) ((x - 7) (x - 4))$ .

$\frac{x ((x (x + 8)) ((x - 7) (x - 4)))}{(x - 7) (x + 8) (4 x)}$

Step 4.2.2

Cancel the common factors.

Tap for more steps...

Step 4.2.2.1

Factor $x$ out of $(x - 7) (x + 8) (4 x)$ .

$\frac{x ((x (x + 8)) ((x - 7) (x - 4)))}{x ((x - 7) (x + 8) \cdot (4))}$

Step 4.2.2.2

Cancel the common factor.

$\frac{x ((x (x + 8)) ((x - 7) (x - 4)))}{x ((x - 7) (x + 8) \cdot (4))}$

Step 4.2.2.3

Rewrite the expression.

$\frac{(x (x + 8)) ((x - 7) (x - 4))}{(x - 7) (x + 8) \cdot (4)}$

Step 4.3

Cancel the common factor of $x + 8$ .

Tap for more steps...

Step 4.3.1

Cancel the common factor.

$\frac{x (x + 8) ((x - 7) (x - 4))}{(x - 7) (x + 8) \cdot 4}$

Step 4.3.2

Rewrite the expression.

$\frac{(x) ((x - 7) (x - 4))}{(x - 7) \cdot (4)}$

Step 4.4

Cancel the common factor of $x - 7$ .

Tap for more steps...

Step 4.4.1

Cancel the common factor.

$\frac{x ((x - 7) (x - 4))}{(x - 7) \cdot 4}$

Step 4.4.2

Rewrite the expression.

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

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