Using the identity $(a - b)^{2} = a^{2} - 2 a b + b^{2}$ ,compute $(5 a - 4 b)^{2}$ ;

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Solution

Using $(a - b)^{2} = a^{2} - 2 a b + b^{2}$ ,
$(5 a - 4 b)^{2} = (5 a)^{2} - 2 (5 a \times 4 b) + (4 b)^{2}$
$= 25 a^{2} - 2 (20 a b) + 16 b^{2}$
$= 25 a^{2} - 40 a b + 16 b^{2}$

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