Toolkit 6

Square of a sum

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

Proof

Using the distributive law,

\begin{aligned} (a+b)^2 &= (a+b)(a+b) \\ &= a^2 + ab + ba + b^2 \\ &= a^2 + 2ab + b^2. \quad\square \end{aligned}