Question

${\text{a}}^2{\text{+b}}^2$ is equal to what ?

Answer 1

We can write $({\text{a+b)}}^2{\text{=(a+b)(a+b)=a}}^2{\text{+ab+ba+b}}^2$

$$\begin{gathered} ={\text{a}}^2{\text{+ab+ab+b}}^2\text{(because ab=ba)} \\ ={\text{a}}^2{\text{+2ab+b}}^2 \end{gathered}$$

${\text{⇒a}}^2{\text{+b}}^2{\text{=(a+b)}}^2\text{-2ab (after tranposing the values)}$

Hence ${\text{a}}^2{\text{+b}}^2=({\text{a+b)}}^2\text{-2ab}$