Solve for A
A\in \mathrm{R}
Solve for B
B\in \mathrm{R}
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A^{2}+2AB+B^{2}=A^{2}+2AB+B^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(A+B\right)^{2}.
A^{2}+2AB+B^{2}-A^{2}=2AB+B^{2}
Subtract A^{2} from both sides.
2AB+B^{2}=2AB+B^{2}
Combine A^{2} and -A^{2} to get 0.
2AB+B^{2}-2AB=B^{2}
Subtract 2AB from both sides.
B^{2}=B^{2}
Combine 2AB and -2AB to get 0.
\text{true}
Reorder the terms.
A\in \mathrm{R}
This is true for any A.
A^{2}+2AB+B^{2}=A^{2}+2AB+B^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(A+B\right)^{2}.
A^{2}+2AB+B^{2}-2AB=A^{2}+B^{2}
Subtract 2AB from both sides.
A^{2}+B^{2}=A^{2}+B^{2}
Combine 2AB and -2AB to get 0.
A^{2}+B^{2}-B^{2}=A^{2}
Subtract B^{2} from both sides.
A^{2}=A^{2}
Combine B^{2} and -B^{2} to get 0.
\text{true}
Reorder the terms.
B\in \mathrm{R}
This is true for any B.
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