Expand $(l + m)^{2} - (l - m)^{2}$

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Solution

We know that,
$(a + b)^{2} = a^{2} + 2 a b + b^{2}$ and
$(a - b)^{2} = a^{2} - 2 a b + b^{2}$
Now, lets evaluate $(l + m)^{2} - (l - m)^{2}$
$(l + m)^{2} - (l - m)^{2}$
$= (l^{2} + 2 l m + m^{2}) - (l^{2} - 2 l m + m^{2})$
$= l^{2} + 2 l m + m^{2} - l^{2} + 2 l m - m^{2}$
$= 4 l m$
$∴ (l + m)^{2} - (l - m)^{2} = 4 l m$

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