Solve (a+b)^2=(a-b)^2+c

$$( a + b ) ^ { 2 } = ( a - b ) ^ { 2 } + c$$

Solve for a

$$\left\{\begin{matrix}a=\frac{c}{4b}\text{, }&b\neq 0\\a\in \mathrm{R}\text{, }&c=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+b\right)^{2}.

$$a^{2}+2ab+b^{2}=\left(a-b\right)^{2}+c$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.

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

Subtract a^{2} from both sides.

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

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

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

Add 2ab to both sides.

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

Combine 2ab and 2ab to get 4ab.

$$4ab+b^{2}=b^{2}+c$$

Subtract b^{2} from both sides.

$$4ab=b^{2}+c-b^{2}$$

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

$$4ab=c$$

The equation is in standard form.

$$4ba=c$$

Divide both sides by 4b.

$$\frac{4ba}{4b}=\frac{c}{4b}$$

Dividing by 4b undoes the multiplication by 4b.

$$a=\frac{c}{4b}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{c}{4a}\text{, }&a\neq 0\\b\in \mathrm{R}\text{, }&c=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+b\right)^{2}.

$$a^{2}+2ab+b^{2}=\left(a-b\right)^{2}+c$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-b\right)^{2}.

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

Add 2ab to both sides.

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

Combine 2ab and 2ab to get 4ab.

$$a^{2}+4ab+b^{2}=a^{2}+b^{2}+c$$

Subtract b^{2} from both sides.

$$a^{2}+4ab+b^{2}-b^{2}=a^{2}+c$$

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

$$a^{2}+4ab=a^{2}+c$$

Subtract a^{2} from both sides.

$$4ab=a^{2}+c-a^{2}$$

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

$$4ab=c$$

Divide both sides by 4a.

$$\frac{4ab}{4a}=\frac{c}{4a}$$

Dividing by 4a undoes the multiplication by 4a.

$$b=\frac{c}{4a}$$