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

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

Evaluate

$$\left(x+y\right)\left(x-y+2\right)$$

Solution Steps

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

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

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

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

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

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

Subtract 1 from 1 to get 0.

$$x^{2}+2x-y^{2}+2y$$

Expand

$$x^{2}+2x-y^{2}+2y$$

Solution Steps

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

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

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

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

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

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

Subtract 1 from 1 to get 0.

$$x^{2}+2x-y^{2}+2y$$