To prove the equation \(a^2+b^2=(a+b)^2-2ab\), we can start by expanding the right side of the equation:

\((a+b)^2-2ab = (a+b)(a+b) - 2ab\)

Using the distributive property, we can expand further:

\(= a(a+b) + b(a+b) - 2ab\)

\(= a^2 + ab + ab + b^2 - 2ab\)

Now, we can simplify the terms:

\(= a^2 + 2ab + b^2 - 2ab\)

The \(2ab\) and \(-2ab\) terms cancel each other out:

\(= a^2 + b^2\)

Therefore, we have proven that \(a^2+b^2=(a+b)^2-2ab\).