Question

What is $p^2+q^2$ formula?

Answer 1

Expansion of the whole square:

As we know,

${\mathbf{(}\mathbf{a}\mathbf{+}\mathbf{b}\mathbf{)}}^{\mathbf{2}}\mathbf{=}{\mathbf{a}}^{\mathbf{2}}\mathbf{+}{\mathbf{b}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathbf{ab}$

Substitute $a\mathrm{and}b$ with $p\mathrm{and}q$ respectively:

$$\begin{gathered} \therefore {(p+q)}^2=p^2+q^2+2pq \\ \Rightarrow p^2+q^2={(p+q)}^2-2pq \end{gathered}$$

Hence the formula ${\mathbf{\text{p}}}^{\mathbf{2}}\mathbf{+}{\mathbf{q}}^{\mathbf{2}}\mathbf{=}{\mathbf{(}\mathbf{p}\mathbf{+}\mathbf{q}\mathbf{)}}^{\mathbf{2}}\mathbf{-}\mathbf{2}\mathbf{pq}$.