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

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

Evaluate

$$0$$

Solution Steps

Multiply x+y and x+y to get \left(x+y\right)^{2}.

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

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

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

Use the distributive property to multiply x by x^{2}+2xy+y^{2}.

$$x^{3}+2yx^{2}+xy^{2}-x\left(x+y\right)^{2}$$

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

$$x^{3}+2yx^{2}+xy^{2}-x\left(x^{2}+2xy+y^{2}\right)$$

Use the distributive property to multiply x by x^{2}+2xy+y^{2}.

$$x^{3}+2yx^{2}+xy^{2}-\left(x^{3}+2yx^{2}+xy^{2}\right)$$

Combine x^{3}+2yx^{2}+xy^{2} and -\left(x^{3}+2yx^{2}+xy^{2}\right) to get 0.

$$0$$

Factor

$$0$$

Solution Steps

Factor out common term x by using distributive property.

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

Consider \left(x+y\right)\left(x+y\right)-\left(x+y\right)^{2}. Simplify.

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