Factorize the following algebraic expression: $25 x^{2} - 10 x + 1 - 36 y^{2}$

(5 x - 6 y - 1) (5 x - 6 y + 1)

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(5 x + 6 y - 1) (5 x - 6 y - 1)

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6 y (5 x - 1) (5 x + 1)

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None of the above

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Solution

The correct option is B $(5 x + 6 y - 1) (5 x - 6 y - 1)$
$25 x^{2} - 10 x + 1 - 36 y^{2} = (5 x)^{2} - 2 \times 5 x \times 1 + (1)^{2} - (6 y)^{2} {\begin{matrix} a^{2} - 2 a b + b^{2} = (a - b)^{2} and a^{2} - b^{2} = (a + b) (a - b) \end{matrix} = (5 x - 1)^{2} - (6 y)^{2} = (5 x - 1 + 6 y) (5 x - 1 - 6 y) = (5 x + 6 y - 1) (5 x - 6 y - 1)$

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