Solve a^2+b^2=a^2-2ab+b^2

$$a ^ { 2 } + b ^ { 2 } = a ^ { 2 } - 2 a b + b ^ { 2 }$$

Solve for a

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

Steps for Solving Linear Equation

Subtract a^{2} from both sides.

$$a^{2}+b^{2}-a^{2}=-2ab+b^{2}$$

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

$$b^{2}=-2ab+b^{2}$$

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

$$-2ab+b^{2}=b^{2}$$

Subtract b^{2} from both sides.

$$-2ab=b^{2}-b^{2}$$

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

$$-2ab=0$$

The equation is in standard form.

$$\left(-2b\right)a=0$$

Divide 0 by -2b.

$$a=0$$

Solve for b

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

Steps for Solving Linear Equation

Add 2ab to both sides.

$$a^{2}+b^{2}+2ab=a^{2}+b^{2}$$

Subtract b^{2} from both sides.

$$a^{2}+b^{2}+2ab-b^{2}=a^{2}$$

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

$$a^{2}+2ab=a^{2}$$

Subtract a^{2} from both sides.

$$2ab=a^{2}-a^{2}$$

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

$$2ab=0$$

Divide 0 by 2a.

$$b=0$$