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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

To find the opposite of x^{2}+2x+1, find the opposite of each term.

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

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

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

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

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

Subtract 1 from 2 to get 1.

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

Expand

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

Solution Steps

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

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

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

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

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

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

To find the opposite of x^{2}+2x+1, find the opposite of each term.

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

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

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

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

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

Subtract 1 from 2 to get 1.

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