Simplify (2x^5-200x^3)/(4x^4-64x^3+240x^2)*(x-6)/(x+10)

$\frac{2 x^{5} - 200 x^{3}}{4 x^{4} - 64 x^{3} + 240 x^{2}} \cdot \frac{x - 6}{x + 10}$

Step 1

Simplify the numerator.

Factor $2 x^{3}$ out of $2 x^{5} - 200 x^{3}$ .

Factor $2 x^{3}$ out of $2 x^{5}$ .

$\frac{2 x^{3} (x^{2}) - 200 x^{3}}{4 x^{4} - 64 x^{3} + 240 x^{2}} \cdot \frac{x - 6}{x + 10}$

Factor $2 x^{3}$ out of $- 200 x^{3}$ .

$\frac{2 x^{3} (x^{2}) + 2 x^{3} (- 100)}{4 x^{4} - 64 x^{3} + 240 x^{2}} \cdot \frac{x - 6}{x + 10}$

Factor $2 x^{3}$ out of $2 x^{3} (x^{2}) + 2 x^{3} (- 100)$ .

$\frac{2 x^{3} (x^{2} - 100)}{4 x^{4} - 64 x^{3} + 240 x^{2}} \cdot \frac{x - 6}{x + 10}$

Rewrite $100$ as $10^{2}$ .

$\frac{2 x^{3} (x^{2} - 10^{2})}{4 x^{4} - 64 x^{3} + 240 x^{2}} \cdot \frac{x - 6}{x + 10}$

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 $b = 10$ .

$\frac{2 x^{3} (x + 10) (x - 10)}{4 x^{4} - 64 x^{3} + 240 x^{2}} \cdot \frac{x - 6}{x + 10}$

Step 2

Simplify the denominator.

Factor $4 x^{2}$ out of $4 x^{4} - 64 x^{3} + 240 x^{2}$ .

Factor $4 x^{2}$ out of $4 x^{4}$ .

$\frac{2 x^{3} (x + 10) (x - 10)}{4 x^{2} (x^{2}) - 64 x^{3} + 240 x^{2}} \cdot \frac{x - 6}{x + 10}$

Factor $4 x^{2}$ out of $- 64 x^{3}$ .

$\frac{2 x^{3} (x + 10) (x - 10)}{4 x^{2} (x^{2}) + 4 x^{2} (- 16 x) + 240 x^{2}} \cdot \frac{x - 6}{x + 10}$

Factor $4 x^{2}$ out of $240 x^{2}$ .

$\frac{2 x^{3} (x + 10) (x - 10)}{4 x^{2} (x^{2}) + 4 x^{2} (- 16 x) + 4 x^{2} (60)} \cdot \frac{x - 6}{x + 10}$

Factor $4 x^{2}$ out of $4 x^{2} (x^{2}) + 4 x^{2} (- 16 x)$ .

$\frac{2 x^{3} (x + 10) (x - 10)}{4 x^{2} (x^{2} - 16 x) + 4 x^{2} (60)} \cdot \frac{x - 6}{x + 10}$

Factor $4 x^{2}$ out of $4 x^{2} (x^{2} - 16 x) + 4 x^{2} (60)$ .

$\frac{2 x^{3} (x + 10) (x - 10)}{4 x^{2} (x^{2} - 16 x + 60)} \cdot \frac{x - 6}{x + 10}$

Factor $x^{2} - 16 x + 60$ 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 $60$ and whose sum is $- 16$ .

$- 10, - 6$

Write the factored form using these integers.

$\frac{2 x^{3} (x + 10) (x - 10)}{4 x^{2} ((x - 10) (x - 6))} \cdot \frac{x - 6}{x + 10}$

$\frac{2 x^{3} (x + 10) (x - 10)}{4 x^{2} (x - 10) (x - 6)} \cdot \frac{x - 6}{x + 10}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x + 10$ .

Factor $x + 10$ out of $2 x^{3} (x + 10) (x - 10)$ .

$\frac{(x + 10) (2 x^{3} (x - 10))}{4 x^{2} (x - 10) (x - 6)} \cdot \frac{x - 6}{x + 10}$

Cancel the common factor.

$\frac{(x + 10) (2 x^{3} (x - 10))}{4 x^{2} (x - 10) (x - 6)} \cdot \frac{x - 6}{x + 10}$

Rewrite the expression.

$\frac{2 x^{3} (x - 10)}{4 x^{2} (x - 10) (x - 6)} \cdot (x - 6)$

Cancel the common factor of $x - 6$ .

Factor $x - 6$ out of $4 x^{2} (x - 10) (x - 6)$ .

$\frac{2 x^{3} (x - 10)}{(x - 6) (4 x^{2} (x - 10))} \cdot (x - 6)$

Cancel the common factor.

$\frac{2 x^{3} (x - 10)}{(x - 6) (4 x^{2} (x - 10))} \cdot (x - 6)$

Rewrite the expression.

$\frac{2 x^{3} (x - 10)}{4 x^{2} (x - 10)}$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 x^{3} (x - 10)$ .

$\frac{2 (x^{3} (x - 10))}{4 x^{2} (x - 10)}$

Cancel the common factors.

Factor $2$ out of $4 x^{2} (x - 10)$ .

$\frac{2 (x^{3} (x - 10))}{2 (2 x^{2} (x - 10))}$

Cancel the common factor.

$\frac{2 (x^{3} (x - 10))}{2 (2 x^{2} (x - 10))}$

Rewrite the expression.

$\frac{x^{3} (x - 10)}{2 x^{2} (x - 10)}$

Cancel the common factor of $x^{3}$ and $x^{2}$ .

Factor $x^{2}$ out of $x^{3} (x - 10)$ .

$\frac{x^{2} (x (x - 10))}{2 x^{2} (x - 10)}$

Cancel the common factors.

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

$\frac{x^{2} (x (x - 10))}{x^{2} (2 (x - 10))}$

Cancel the common factor.

$\frac{x^{2} (x (x - 10))}{x^{2} (2 (x - 10))}$

Rewrite the expression.

$\frac{x (x - 10)}{2 (x - 10)}$

Cancel the common factor of $x - 10$ .

Cancel the common factor.

$\frac{x (x - 10)}{2 (x - 10)}$

Rewrite the expression.

$\frac{x}{2}$

Simplify (2x^5-200x^3)/(4x^4-64x^3+240x^2)*(x-6)/(x+10)

Related Questions

Support LCMGCF.com by disabling your adblocker.