Simplify (6x^2-600)/(3x-30)*(x^2-100)/(x^2(x+10)^2)

$\frac{6 x^{2} - 600}{3 x - 30} \cdot \frac{x^{2} - 100}{x^{2} {(x + 10)}^{2}}$

Simplify the numerator.

Factor $6$ out of $6 x^{2} - 600$ .

Factor $6$ out of $6 x^{2}$ .

$\frac{6 (x^{2}) - 600}{3 x - 30} \cdot \frac{x^{2} - 100}{x^{2} {(x + 10)}^{2}}$

Factor $6$ out of $- 600$ .

$\frac{6 x^{2} + 6 \cdot - 100}{3 x - 30} \cdot \frac{x^{2} - 100}{x^{2} {(x + 10)}^{2}}$

Factor $6$ out of $6 x^{2} + 6 \cdot - 100$ .

$\frac{6 (x^{2} - 100)}{3 x - 30} \cdot \frac{x^{2} - 100}{x^{2} {(x + 10)}^{2}}$

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

$\frac{6 (x^{2} - 10^{2})}{3 x - 30} \cdot \frac{x^{2} - 100}{x^{2} {(x + 10)}^{2}}$

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 $b = 10$ .

$\frac{6 (x + 10) (x - 10)}{3 x - 30} \cdot \frac{x^{2} - 100}{x^{2} {(x + 10)}^{2}}$

Factor $3$ out of $3 x - 30$ .

Factor $3$ out of $3 x$ .

$\frac{6 (x + 10) (x - 10)}{3 (x) - 30} \cdot \frac{x^{2} - 100}{x^{2} {(x + 10)}^{2}}$

Factor $3$ out of $- 30$ .

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

Factor $3$ out of $3 x + 3 \cdot - 10$ .

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

Simplify the numerator.

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

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

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 $b = 10$ .

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

Simplify terms.

Combine.

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

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 (x + 10) (x - 10) ((x + 10) (x - 10))$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + 10$ and ${(x + 10)}^{2}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 10$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + 10$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

Simplify (6x^2-600)/(3x-30)*(x^2-100)/(x^2(x+10)^2)

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