Question

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

Answer 1

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

Rewrite the expression ${\left(a+b\right)}^2$:

${\left(a+b\right)}^2=\left(a+b\right)\left(a+b\right)$

Use the distributive formula: $z(x+y)=zx+zy$ to simplify further:

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

Hence, the formula is $\begin{array}{rcl}{\left(a+b\right)}^2& =& a^2+2ab+b^2\end{array}$.