Solve (a+b)^2=a^2+8b+b^2

$$( a + b ) ^ { 2 } = a ^ { 2 } + 8 b + b ^ { 2 }$$

Solve for a

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

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}.

$$a^{2}+2ab+b^{2}=a^{2}+8b+b^{2}$$

Subtract a^{2} from both sides.

$$a^{2}+2ab+b^{2}-a^{2}=8b+b^{2}$$

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

$$2ab+b^{2}=8b+b^{2}$$

Subtract b^{2} from both sides.

$$2ab=8b+b^{2}-b^{2}$$

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

$$2ab=8b$$

The equation is in standard form.

$$2ba=8b$$

Divide both sides by 2b.

$$\frac{2ba}{2b}=\frac{8b}{2b}$$

Dividing by 2b undoes the multiplication by 2b.

$$a=\frac{8b}{2b}$$

Divide 8b by 2b.

$$a=4$$

Solve for b

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

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}.

$$a^{2}+2ab+b^{2}=a^{2}+8b+b^{2}$$

Subtract 8b from both sides.

$$a^{2}+2ab+b^{2}-8b=a^{2}+b^{2}$$

Subtract b^{2} from both sides.

$$a^{2}+2ab+b^{2}-8b-b^{2}=a^{2}$$

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

$$a^{2}+2ab-8b=a^{2}$$

Subtract a^{2} from both sides.

$$2ab-8b=a^{2}-a^{2}$$

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

$$2ab-8b=0$$

Combine all terms containing b.

$$\left(2a-8\right)b=0$$

Divide 0 by 2a-8.

$$b=0$$