Simplify (2a^3-32a)/(2a^3+16a^2+32a)

$\frac{2 a^{3} - 32 a}{2 a^{3} + 16 a^{2} + 32 a}$

Simplify the numerator.

Factor $2 a$ out of $2 a^{3} - 32 a$ .

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

$\frac{2 a (a^{2}) - 32 a}{2 a^{3} + 16 a^{2} + 32 a}$

Factor $2 a$ out of $- 32 a$ .

$\frac{2 a (a^{2}) + 2 a (- 16)}{2 a^{3} + 16 a^{2} + 32 a}$

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

$\frac{2 a (a^{2} - 16)}{2 a^{3} + 16 a^{2} + 32 a}$

Rewrite $16$ as $4^{2}$ .

$\frac{2 a (a^{2} - 4^{2})}{2 a^{3} + 16 a^{2} + 32 a}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = 4$ .

$\frac{2 a (a + 4) (a - 4)}{2 a^{3} + 16 a^{2} + 32 a}$

Simplify the denominator.

Factor $2 a$ out of $2 a^{3} + 16 a^{2} + 32 a$ .

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

$\frac{2 a (a + 4) (a - 4)}{2 a (a^{2}) + 16 a^{2} + 32 a}$

Factor $2 a$ out of $16 a^{2}$ .

$\frac{2 a (a + 4) (a - 4)}{2 a (a^{2}) + 2 a (8 a) + 32 a}$

Factor $2 a$ out of $32 a$ .

$\frac{2 a (a + 4) (a - 4)}{2 a (a^{2}) + 2 a (8 a) + 2 a (16)}$

Factor $2 a$ out of $2 a (a^{2}) + 2 a (8 a)$ .

$\frac{2 a (a + 4) (a - 4)}{2 a (a^{2} + 8 a) + 2 a (16)}$

Factor $2 a$ out of $2 a (a^{2} + 8 a) + 2 a (16)$ .

$\frac{2 a (a + 4) (a - 4)}{2 a (a^{2} + 8 a + 16)}$

Factor using the perfect square rule.

Rewrite $16$ as $4^{2}$ .

$\frac{2 a (a + 4) (a - 4)}{2 a (a^{2} + 8 a + 4^{2})}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 a = 2 \cdot a \cdot 4$

Rewrite the polynomial.

$\frac{2 a (a + 4) (a - 4)}{2 a (a^{2} + 2 \cdot a \cdot 4 + 4^{2})}$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = a$ and $b = 4$ .

$\frac{2 a (a + 4) (a - 4)}{2 a {(a + 4)}^{2}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a (a + 4) (a - 4)}{2 a {(a + 4)}^{2}}$

Rewrite the expression.

$\frac{(a (a + 4)) (a - 4)}{a {(a + 4)}^{2}}$

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{a (a + 4) (a - 4)}{a {(a + 4)}^{2}}$

Rewrite the expression.

$\frac{(a + 4) (a - 4)}{{(a + 4)}^{2}}$

Cancel the common factors.

Factor $a + 4$ out of ${(a + 4)}^{2}$ .

$\frac{(a + 4) (a - 4)}{(a + 4) (a + 4)}$

Cancel the common factor.

$\frac{(a + 4) (a - 4)}{(a + 4) (a + 4)}$

Rewrite the expression.

$\frac{a - 4}{a + 4}$

Simplify (2a^3-32a)/(2a^3+16a^2+32a)

Related Questions

Support LCMGCF.com by disabling your adblocker.