Algebraic Identities

Perfect Square

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

Difference of Two Squares

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

Proof of \((a+b)^2 = a^2 + 2ab + b^2\)

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

Proof of \(a^2 - b^2 = (a+b)(a-b)\)

Clarification to the retained image: \(a^2+b^2\) does have identities, for example \(a^2+b^2=(a+b)^2-2ab\). It does not have the difference-of-squares factorisation \((a+b)(a-b)\). In general, \((a+b)^2\ne a^2+b^2\) and \((a-b)^2\ne a^2-b^2\); keep the middle term.