Simplify :
$(8 a - 5 b)^{2}$

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Solution

We will use ${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$ to simplify the given expression.

${(8 a - 5 b)}^{2} = {(8 a)}^{2} - 2 (8 a) (5 b) + {(5 b)}^{2}$
$= 64 a^{2} - 80 a b + 25 b^{2}$

Hence the given expression simplifies to $64 a^{2} - 40 a b + 25 b^{2} .$

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