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

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

Evaluate

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

Solution Steps

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

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

Consider \left(x+y\right)\left(x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

$$xy-y^{2}$$

Expand

$$xy-y^{2}$$

Solution Steps

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

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

Consider \left(x+y\right)\left(x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

$$xy-y^{2}$$