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

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

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=y\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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}.

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

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

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

Subtract x^{2} from both sides.

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

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

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract y^{2} from both sides.

$$-2xy=-y^{2}-y^{2}$$

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

$$-2xy=-2y^{2}$$

Cancel out -2 on both sides.

$$xy=y^{2}$$

The equation is in standard form.

$$yx=y^{2}$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{y^{2}}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{y^{2}}{y}$$

Divide y^{2} by y.

$$x=y$$

Solve for x

$$\left\{\begin{matrix}\\x=y\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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}.

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

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

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

Subtract x^{2} from both sides.

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

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

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract y^{2} from both sides.

$$-2xy=-y^{2}-y^{2}$$

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

$$-2xy=-2y^{2}$$

Cancel out -2 on both sides.

$$xy=y^{2}$$

The equation is in standard form.

$$yx=y^{2}$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{y^{2}}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{y^{2}}{y}$$

Divide y^{2} by y.

$$x=y$$

Solve for y

$$y=x$$

$$y=0$$