Simplify (x^2-64)/(x^2)*(x^2-8x)/(x^2+x-72)

$\frac{x^{2} - 64}{x^{2}} \cdot \frac{x^{2} - 8 x}{x^{2} + x - 72}$

Step 1

Simplify the numerator.

Rewrite $64$ as $8^{2}$ .

$\frac{x^{2} - 8^{2}}{x^{2}} \cdot \frac{x^{2} - 8 x}{x^{2} + x - 72}$

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 $b = 8$ .

$\frac{(x + 8) (x - 8)}{x^{2}} \cdot \frac{x^{2} - 8 x}{x^{2} + x - 72}$

Step 2

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

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

$\frac{(x + 8) (x - 8)}{x^{2}} \cdot \frac{x \cdot x - 8 x}{x^{2} + x - 72}$

Factor $x$ out of $- 8 x$ .

$\frac{(x + 8) (x - 8)}{x^{2}} \cdot \frac{x \cdot x + x \cdot - 8}{x^{2} + x - 72}$

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

$\frac{(x + 8) (x - 8)}{x^{2}} \cdot \frac{x (x - 8)}{x^{2} + x - 72}$

Step 3

Factor $x^{2} + x - 72$ 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 $- 72$ and whose sum is $1$ .

$- 8, 9$

Write the factored form using these integers.

$\frac{(x + 8) (x - 8)}{x^{2}} \cdot \frac{x (x - 8)}{(x - 8) (x + 9)}$

Step 4

Simplify terms.

Combine.

$\frac{(x + 8) (x - 8) (x (x - 8))}{x^{2} ((x - 8) (x + 9))}$

Cancel the common factor of $x - 8$ .

Cancel the common factor.

$\frac{(x + 8) (x - 8) (x (x - 8))}{x^{2} ((x - 8) (x + 9))}$

Rewrite the expression.

$\frac{(x + 8) (x (x - 8))}{x^{2} (x + 9)}$

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

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

$\frac{x ((x + 8) (x - 8))}{x^{2} (x + 9)}$

Cancel the common factors.

Factor $x$ out of $x^{2} (x + 9)$ .

$\frac{x ((x + 8) (x - 8))}{x (x (x + 9))}$

Cancel the common factor.

$\frac{x ((x + 8) (x - 8))}{x (x (x + 9))}$

Rewrite the expression.

$\frac{(x + 8) (x - 8)}{x (x + 9)}$

Simplify (x^2-64)/(x^2)*(x^2-8x)/(x^2+x-72)

Related Questions

Support LCMGCF.com by disabling your adblocker.