Factorise: $81 x^{2} - 198 x y + 121 y^{2}$

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Solution

The given polynomial $81 x^{2} - 198 x y + 121 y^{2}$ can be factorized as follows:

$81 x^{2} - 198 x y + 121 y^{2} = (9 x)^{2} - (2 \times 9 x \times 11 y) + (11 y)^{2} = (9 x - 11 y)^{2} (∵ (a - b)^{2} = a^{2} + b^{2} - 2 a b)$

Hence, $81 x^{2} - 198 x y + 121 y^{2} = (9 x - 11 y)^{2}$ .

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