Question

What is the formula of ${\left(a+b\right)}^2$?

Answer 1

Derive the formula for${\left(a+b\right)}^2$.

${\left(a+b\right)}^2$ can be written as:

$\begin{array}{rcl}{\left(a+b\right)}^{\mathbf{2}}& \mathbf{=}& \left(a+b\right)\left(a+b\right)\end{array}$

To simplify, apply the distributive property of multiplication i.e.$\begin{array}{rcl}z(x+y)& =& zx+zy\end{array}$ :

$\begin{array}{rcl}{\left(a+b\right)}^2& =& a\left(a+b\right)+b\left(a+b\right)\\ & =& a^2+ab+ab+b^2\\ & =& a^2+2ab+b^2\end{array}$

Hence, the formula is ${(a+b)}^2=a^2+2ab+b^2$