Solve 2(-4-x)+x^2left(x-1right)^2-6

$$2(-4-x)+ { x }^{ 2 } { \left(x-1 \right) }^{ 2 } -6$$

Evaluate

$$\left(x\left(x-1\right)\right)^{2}-2x-14$$

Solution Steps

Use the distributive property to multiply 2 by -4-x.

$$-8-2x+x^{2}\left(x-1\right)^{2}-6$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$-8-2x+x^{2}\left(x^{2}-2x+1\right)-6$$

Use the distributive property to multiply x^{2} by x^{2}-2x+1.

$$-8-2x+x^{4}-2x^{3}+x^{2}-6$$

Subtract 6 from -8 to get -14.

$$-14-2x+x^{4}-2x^{3}+x^{2}$$

Expand

$$x^{4}-2x^{3}+x^{2}-2x-14$$

Solution Steps

Use the distributive property to multiply 2 by -4-x.

$$-8-2x+x^{2}\left(x-1\right)^{2}-6$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$-8-2x+x^{2}\left(x^{2}-2x+1\right)-6$$

Use the distributive property to multiply x^{2} by x^{2}-2x+1.

$$-8-2x+x^{4}-2x^{3}+x^{2}-6$$

Subtract 6 from -8 to get -14.

$$-14-2x+x^{4}-2x^{3}+x^{2}$$