Solve (-2x)^3(2x^3-1/2x-1)-2x(2x^3+4x^2)

$$( - 2 x ) ^ { 3 } ( 2 x ^ { 3 } - \frac { 1 } { 2 } x - 1 ) - 2 x ( 2 x ^ { 3 } + 4 x ^ { 2 } )$$

Evaluate

$$-16x^{6}$$

Solution Steps

Expand \left(-2x\right)^{3}.

$$\left(-2\right)^{3}x^{3}\left(2x^{3}-\frac{1}{2}x-1\right)-2x\left(2x^{3}+4x^{2}\right)$$

Calculate -2 to the power of 3 and get -8.

$$-8x^{3}\left(2x^{3}-\frac{1}{2}x-1\right)-2x\left(2x^{3}+4x^{2}\right)$$

Use the distributive property to multiply -8x^{3} by 2x^{3}-\frac{1}{2}x-1.

$$-16x^{6}+4x^{4}+8x^{3}-2x\left(2x^{3}+4x^{2}\right)$$

Use the distributive property to multiply -2x by 2x^{3}+4x^{2}.

$$-16x^{6}+4x^{4}+8x^{3}-4x^{4}-8x^{3}$$

Combine 4x^{4} and -4x^{4} to get 0.

$$-16x^{6}+8x^{3}-8x^{3}$$

Combine 8x^{3} and -8x^{3} to get 0.

$$-16x^{6}$$

Expand

$$-16x^{6}$$

Solution Steps

Expand \left(-2x\right)^{3}.

$$\left(-2\right)^{3}x^{3}\left(2x^{3}-\frac{1}{2}x-1\right)-2x\left(2x^{3}+4x^{2}\right)$$

Calculate -2 to the power of 3 and get -8.

$$-8x^{3}\left(2x^{3}-\frac{1}{2}x-1\right)-2x\left(2x^{3}+4x^{2}\right)$$

Use the distributive property to multiply -8x^{3} by 2x^{3}-\frac{1}{2}x-1.

$$-16x^{6}+4x^{4}+8x^{3}-2x\left(2x^{3}+4x^{2}\right)$$

Use the distributive property to multiply -2x by 2x^{3}+4x^{2}.

$$-16x^{6}+4x^{4}+8x^{3}-4x^{4}-8x^{3}$$

Combine 4x^{4} and -4x^{4} to get 0.

$$-16x^{6}+8x^{3}-8x^{3}$$

Combine 8x^{3} and -8x^{3} to get 0.

$$-16x^{6}$$