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

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

Evaluate

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

Solution Steps

Calculate x to the power of 1 and get x.

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

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

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

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

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

Use the distributive property to multiply -2x^{2}-4x-2 by x^{2}+1 and combine like terms.

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

Use the distributive property to multiply -2x^{4}-4x^{2}-4x^{3}-4x-2 by x-1 and combine like terms.

$$-2x^{5}-2x^{4}+2x+2$$

Expand

$$2+2x-2x^{4}-2x^{5}$$

Solution Steps

Calculate x to the power of 1 and get x.

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

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

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

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

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

Use the distributive property to multiply -2x^{2}-4x-2 by x^{2}+1 and combine like terms.

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

Use the distributive property to multiply -2x^{4}-4x^{2}-4x^{3}-4x-2 by x-1 and combine like terms.

$$-2x^{5}-2x^{4}+2x+2$$