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

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

Evaluate

$$x^{3}+2x^{2}-7x+2$$

Solution Steps

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

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

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

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

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

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

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

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

Combine -4x and -3x to get -7x.

$$2x^{2}-7x+2+x^{3}+2-2$$

Add 2 and 2 to get 4.

$$2x^{2}-7x+4+x^{3}-2$$

Subtract 2 from 4 to get 2.

$$2x^{2}-7x+2+x^{3}$$

Expand

$$x^{3}+2x^{2}-7x+2$$

Solution Steps

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

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

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

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

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

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

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

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

Combine -4x and -3x to get -7x.

$$2x^{2}-7x+2+x^{3}+2-2$$

Add 2 and 2 to get 4.

$$2x^{2}-7x+4+x^{3}-2$$

Subtract 2 from 4 to get 2.

$$2x^{2}-7x+2+x^{3}$$