Simplify (10x^2-40)/(5x^2-25x-70)*(x^3-7x^2)/(x-2)

$\frac{10 x^{2} - 40}{5 x^{2} - 25 x - 70} \cdot \frac{x^{3} - 7 x^{2}}{x - 2}$

Simplify the numerator.

Factor $10$ out of $10 x^{2} - 40$ .

Factor $10$ out of $10 x^{2}$ .

$\frac{10 (x^{2}) - 40}{5 x^{2} - 25 x - 70} \cdot \frac{x^{3} - 7 x^{2}}{x - 2}$

Factor $10$ out of $- 40$ .

$\frac{10 x^{2} + 10 \cdot - 4}{5 x^{2} - 25 x - 70} \cdot \frac{x^{3} - 7 x^{2}}{x - 2}$

Factor $10$ out of $10 x^{2} + 10 \cdot - 4$ .

$\frac{10 (x^{2} - 4)}{5 x^{2} - 25 x - 70} \cdot \frac{x^{3} - 7 x^{2}}{x - 2}$

Rewrite $4$ as $2^{2}$ .

$\frac{10 (x^{2} - 2^{2})}{5 x^{2} - 25 x - 70} \cdot \frac{x^{3} - 7 x^{2}}{x - 2}$

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 $b = 2$ .

$\frac{10 (x + 2) (x - 2)}{5 x^{2} - 25 x - 70} \cdot \frac{x^{3} - 7 x^{2}}{x - 2}$

Simplify the denominator.

Factor $5$ out of $5 x^{2} - 25 x - 70$ .

Factor $5$ out of $5 x^{2}$ .

$\frac{10 (x + 2) (x - 2)}{5 (x^{2}) - 25 x - 70} \cdot \frac{x^{3} - 7 x^{2}}{x - 2}$

Factor $5$ out of $- 25 x$ .

$\frac{10 (x + 2) (x - 2)}{5 (x^{2}) + 5 (- 5 x) - 70} \cdot \frac{x^{3} - 7 x^{2}}{x - 2}$

Factor $5$ out of $- 70$ .

$\frac{10 (x + 2) (x - 2)}{5 x^{2} + 5 (- 5 x) + 5 \cdot - 14} \cdot \frac{x^{3} - 7 x^{2}}{x - 2}$

Factor $5$ out of $5 x^{2} + 5 (- 5 x)$ .

$\frac{10 (x + 2) (x - 2)}{5 (x^{2} - 5 x) + 5 \cdot - 14} \cdot \frac{x^{3} - 7 x^{2}}{x - 2}$

Factor $5$ out of $5 (x^{2} - 5 x) + 5 \cdot - 14$ .

$\frac{10 (x + 2) (x - 2)}{5 (x^{2} - 5 x - 14)} \cdot \frac{x^{3} - 7 x^{2}}{x - 2}$

Factor $x^{2} - 5 x - 14$ 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 $- 14$ and whose sum is $- 5$ .

$- 7, 2$

Write the factored form using these integers.

$\frac{10 (x + 2) (x - 2)}{5 ((x - 7) (x + 2))} \cdot \frac{x^{3} - 7 x^{2}}{x - 2}$

$\frac{10 (x + 2) (x - 2)}{5 (x - 7) (x + 2)} \cdot \frac{x^{3} - 7 x^{2}}{x - 2}$

Simplify terms.

Factor $x^{2}$ out of $x^{3} - 7 x^{2}$ .

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

$\frac{10 (x + 2) (x - 2)}{5 (x - 7) (x + 2)} \cdot \frac{x^{2} x - 7 x^{2}}{x - 2}$

Factor $x^{2}$ out of $- 7 x^{2}$ .

$\frac{10 (x + 2) (x - 2)}{5 (x - 7) (x + 2)} \cdot \frac{x^{2} x + x^{2} \cdot - 7}{x - 2}$

Factor $x^{2}$ out of $x^{2} x + x^{2} \cdot - 7$ .

$\frac{10 (x + 2) (x - 2)}{5 (x - 7) (x + 2)} \cdot \frac{x^{2} (x - 7)}{x - 2}$

Cancel the common factor of $x - 2$ .

Factor $x - 2$ out of $10 (x + 2) (x - 2)$ .

$\frac{(x - 2) (10 (x + 2))}{5 (x - 7) (x + 2)} \cdot \frac{x^{2} (x - 7)}{x - 2}$

Cancel the common factor.

$\frac{(x - 2) (10 (x + 2))}{5 (x - 7) (x + 2)} \cdot \frac{x^{2} (x - 7)}{x - 2}$

Rewrite the expression.

$\frac{10 (x + 2)}{5 (x - 7) (x + 2)} \cdot (x^{2} (x - 7))$

Cancel the common factor of $x - 7$ .

Factor $x - 7$ out of $5 (x - 7) (x + 2)$ .

$\frac{10 (x + 2)}{(x - 7) (5 (x + 2))} \cdot (x^{2} (x - 7))$

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

$\frac{10 (x + 2)}{(x - 7) (5 (x + 2))} \cdot ((x - 7) x^{2})$

Cancel the common factor.

$\frac{10 (x + 2)}{(x - 7) (5 (x + 2))} \cdot ((x - 7) x^{2})$

Rewrite the expression.

$\frac{10 (x + 2)}{5 (x + 2)} \cdot x^{2}$

Combine $\frac{10 (x + 2)}{5 (x + 2)}$ and $x^{2}$ .

$\frac{10 (x + 2) x^{2}}{5 (x + 2)}$

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $10 (x + 2) x^{2}$ .

$\frac{5 (2 (x + 2) x^{2})}{5 (x + 2)}$

Cancel the common factors.

Cancel the common factor.

$\frac{5 (2 (x + 2) x^{2})}{5 (x + 2)}$

Rewrite the expression.

$\frac{2 (x + 2) x^{2}}{x + 2}$

Cancel the common factor of $x + 2$ .

Cancel the common factor.

$\frac{2 (x + 2) x^{2}}{x + 2}$

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

$2 x^{2}$

Simplify (10x^2-40)/(5x^2-25x-70)*(x^3-7x^2)/(x-2)

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