Question

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

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Solution

## We can write $\left({\text{a+b)}}^{2}{\text{=(a+b)(a+b)=a}}^{2}{\text{+ab+ba+b}}^{2}$ $={\text{a}}^{2}{\text{+ab+ab+b}}^{2}\text{(becauseab=ba)}\phantom{\rule{0ex}{0ex}}={\text{a}}^{2}{\text{+2ab+b}}^{2}$ ${\text{⇒a}}^{2}{\text{+b}}^{2}{\text{=(a+b)}}^{2}\text{-2ab(aftertranposingthevalues)}$Hence ${\text{a}}^{2}{\text{+b}}^{2}=\left({\text{a+b)}}^{2}\text{-2ab}$

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