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

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

Evaluate

$$2$$

Solution Steps

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

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

Use the distributive property to multiply xy-1 by 1+xy and combine like terms.

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

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

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

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

$$-2xy+1+1+2xy$$

Add 1 and 1 to get 2.

$$-2xy+2+2xy$$

Combine -2xy and 2xy to get 0.

$$2$$

Factor

$$2$$