Solve (x+1)^2-(x-1)^2+4x

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

Evaluate

$$8x$$

Solution Steps

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

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

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

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

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

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

Combine x^{2} and -x^{2} to get 0.

$$2x+1+2x-1+4x$$

Combine 2x and 2x to get 4x.

$$4x+1-1+4x$$

Subtract 1 from 1 to get 0.

$$4x+4x$$

Combine 4x and 4x to get 8x.

$$8x$$

Expand

$$8x$$

Solution Steps

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

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

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

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

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

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

Combine x^{2} and -x^{2} to get 0.

$$2x+1+2x-1+4x$$

Combine 2x and 2x to get 4x.

$$4x+1-1+4x$$

Subtract 1 from 1 to get 0.

$$4x+4x$$

Combine 4x and 4x to get 8x.

$$8x$$