Solve (x-2)^2+2(x-2)(x+1)+(x+1)^2=

$$( x - 2 ) ^ { 2 } + 2 ( x - 2 ) ( x + 1 ) + ( x + 1 ) ^ { 2 } =$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

Combine x^{2} and 2x^{2} to get 3x^{2}.

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

Combine -4x and -2x to get -6x.

$$3x^{2}-6x+4-4+\left(x+1\right)^{2}$$

Subtract 4 from 4 to get 0.

$$3x^{2}-6x+\left(x+1\right)^{2}$$

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

$$3x^{2}-6x+x^{2}+2x+1$$

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$4x^{2}-6x+2x+1$$

Combine -6x and 2x to get -4x.

$$4x^{2}-4x+1$$

Expand

$$4x^{2}-4x+1$$

Solution Steps

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

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

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

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

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

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

Combine x^{2} and 2x^{2} to get 3x^{2}.

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

Combine -4x and -2x to get -6x.

$$3x^{2}-6x+4-4+\left(x+1\right)^{2}$$

Subtract 4 from 4 to get 0.

$$3x^{2}-6x+\left(x+1\right)^{2}$$

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

$$3x^{2}-6x+x^{2}+2x+1$$

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$4x^{2}-6x+2x+1$$

Combine -6x and 2x to get -4x.

$$4x^{2}-4x+1$$