Solve 20(7-x^2)^2(-2x)

$$20 ( 7 - x ^ { 2 } ) ^ { 2 } ( - 2 x )$$

Evaluate

$$-40x\left(7-x^{2}\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(7-x^{2}\right)^{2}.

$$20\left(49-14x^{2}+\left(x^{2}\right)^{2}\right)\left(-2\right)x$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$20\left(49-14x^{2}+x^{4}\right)\left(-2\right)x$$

Multiply 20 and -2 to get -40.

$$-40\left(49-14x^{2}+x^{4}\right)x$$

Use the distributive property to multiply -40 by 49-14x^{2}+x^{4}.

$$\left(-1960+560x^{2}-40x^{4}\right)x$$

Use the distributive property to multiply -1960+560x^{2}-40x^{4} by x.

$$-1960x+560x^{3}-40x^{5}$$

Expand

$$-40x^{5}+560x^{3}-1960x$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(7-x^{2}\right)^{2}.

$$20\left(49-14x^{2}+\left(x^{2}\right)^{2}\right)\left(-2\right)x$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$20\left(49-14x^{2}+x^{4}\right)\left(-2\right)x$$

Multiply 20 and -2 to get -40.

$$-40\left(49-14x^{2}+x^{4}\right)x$$

Use the distributive property to multiply -40 by 49-14x^{2}+x^{4}.

$$\left(-1960+560x^{2}-40x^{4}\right)x$$

Use the distributive property to multiply -1960+560x^{2}-40x^{4} by x.

$$-1960x+560x^{3}-40x^{5}$$