Evaluate the following using suitable identity :
${(10 x - 1)}^{2}$
${(x - 8 y)}^{2}$

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Solution

(a) ${(10 x - 1)}^{2} = {(10 x)}^{2} + {(1)}^{2} - 2 \times 10 x \times 1$ (since ${(a - b)}^{2} = a^{2} + b^{2} - 2 a b$ )
$= 100 x^{2} - 20 x + 1$
(b) ${(x - 8 y)}^{2} = {(x)}^{2} + {(8 y)}^{2} - 2 \times x \times 8 y$ ( ${(a - b)}^{2} = a^{2} + b^{2} - 2 a b$ )
$= x^{2} - 16 x y + 64 y^{2}$

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