Simplify (x^3-3x^2)/(x+8)*(x^2-64)/(x^2-11x+24)

$\frac{x^{3} - 3 x^{2}}{x + 8} \cdot \frac{x^{2} - 64}{x^{2} - 11 x + 24}$

Step 1

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

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

$\frac{x^{2} x - 3 x^{2}}{x + 8} \cdot \frac{x^{2} - 64}{x^{2} - 11 x + 24}$

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

$\frac{x^{2} x + x^{2} \cdot - 3}{x + 8} \cdot \frac{x^{2} - 64}{x^{2} - 11 x + 24}$

Factor $x^{2}$ out of $x^{2} x + x^{2} \cdot - 3$ .

$\frac{x^{2} (x - 3)}{x + 8} \cdot \frac{x^{2} - 64}{x^{2} - 11 x + 24}$

Step 2

Simplify the numerator.

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

$\frac{x^{2} (x - 3)}{x + 8} \cdot \frac{x^{2} - 8^{2}}{x^{2} - 11 x + 24}$

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 $b = 8$ .

$\frac{x^{2} (x - 3)}{x + 8} \cdot \frac{(x + 8) (x - 8)}{x^{2} - 11 x + 24}$

Step 3

Factor $x^{2} - 11 x + 24$ 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 $24$ and whose sum is $- 11$ .

$- 8, - 3$

Write the factored form using these integers.

$\frac{x^{2} (x - 3)}{x + 8} \cdot \frac{(x + 8) (x - 8)}{(x - 8) (x - 3)}$

Step 4

Simplify terms.

Cancel the common factor of $x - 3$ .

Factor $x - 3$ out of $x^{2} (x - 3)$ .

$\frac{(x - 3) x^{2}}{x + 8} \cdot \frac{(x + 8) (x - 8)}{(x - 8) (x - 3)}$

Factor $x - 3$ out of $(x - 8) (x - 3)$ .

$\frac{(x - 3) x^{2}}{x + 8} \cdot \frac{(x + 8) (x - 8)}{(x - 3) (x - 8)}$

Cancel the common factor.

$\frac{(x - 3) x^{2}}{x + 8} \cdot \frac{(x + 8) (x - 8)}{(x - 3) (x - 8)}$

Rewrite the expression.

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

Cancel the common factor of $x + 8$ .

Cancel the common factor.

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

Rewrite the expression.

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

Combine $x^{2}$ and $\frac{x - 8}{x - 8}$ .

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

Cancel the common factor of $x - 8$ .

Cancel the common factor.

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

Divide $x^{2}$ by $1$ .

$x^{2}$

Simplify (x^3-3x^2)/(x+8)*(x^2-64)/(x^2-11x+24)

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