Simplify (8x+64)/(x-4)*(x^2-49)/(x^2+x-56)

$\frac{8 x + 64}{x - 4} \cdot \frac{x^{2} - 49}{x^{2} + x - 56}$

Factor $8$ out of $8 x + 64$ .

Factor $8$ out of $8 x$ .

$\frac{8 (x) + 64}{x - 4} \cdot \frac{x^{2} - 49}{x^{2} + x - 56}$

Factor $8$ out of $64$ .

$\frac{8 x + 8 \cdot 8}{x - 4} \cdot \frac{x^{2} - 49}{x^{2} + x - 56}$

Factor $8$ out of $8 x + 8 \cdot 8$ .

$\frac{8 (x + 8)}{x - 4} \cdot \frac{x^{2} - 49}{x^{2} + x - 56}$

Simplify the numerator.

Rewrite $49$ as $7^{2}$ .

$\frac{8 (x + 8)}{x - 4} \cdot \frac{x^{2} - 7^{2}}{x^{2} + x - 56}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 7$ .

$\frac{8 (x + 8)}{x - 4} \cdot \frac{(x + 7) (x - 7)}{x^{2} + x - 56}$

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

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 $1$ .

$- 7, 8$

Write the factored form using these integers.

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

Simplify terms.

Cancel the common factor of $x + 8$ .

Factor $x + 8$ out of $8 (x + 8)$ .

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Cancel the common factor of $x - 7$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (8x+64)/(x-4)*(x^2-49)/(x^2+x-56)

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