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

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

Evaluate

$$xy$$

Solution Steps

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

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

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}.

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

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

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

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

$$yx$$

Expand

$$xy$$

Solution Steps

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

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

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}.

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

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

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

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

$$yx$$