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

$$( 1 ) ( y + 1 ) ( x - y ) - x ( y - x )$$

Evaluate

$$\left(x-y\right)\left(x+y+1\right)$$

Solution Steps

Use the distributive property to multiply 1 by y+1.

$$\left(y+1\right)\left(x-y\right)-x\left(y-x\right)$$

Apply the distributive property by multiplying each term of y+1 by each term of x-y.

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

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

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

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

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

The opposite of -x^{2} is x^{2}.

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

Combine yx and -xy to get 0.

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

Expand

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

Solution Steps

Use the distributive property to multiply 1 by y+1.

$$\left(y+1\right)\left(x-y\right)-x\left(y-x\right)$$

Apply the distributive property by multiplying each term of y+1 by each term of x-y.

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

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

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

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

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

The opposite of -x^{2} is x^{2}.

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

Combine yx and -xy to get 0.

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