Prove $L . H . S = R . H . S$ : $(A + B)^{2} = A^{2} + B^{2} + 2 A B$

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Solution

We have
$\begin{matrix} L . H . S = {(A + B)}^{2} = (A + B) (A + B) = A (A + B) + B (A + B) [B y s i m p l e m u l t i p l i c a t i o n] = A . A + A B + A B + B . B = A^{2} + B^{2} + 2 A B = R . H . S H e n c e L . H . S = R . H . S p o v e d . \end{matrix}$

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