Factorize each of the following algebraic expression:
25x² − 10x + 1 − 36y²

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Solution

$25 x^{2} - 10 x + 1 - 36 y^{2} = (25 x^{2} - 10 x + 1) - 36 y^{2} = [(5 x)^{2} - 2 \times 5 x \times 1 + 1] - 36 y^{2} = (5 x - 1)^{2} - (6 y)^{2} = [(5 x - 1) - 6 y] [(5 x - 1) + 6 y] = (5 x - 1 - 6 y) (5 x - 1 + 6 y) = (5 x - 6 y - 1) (5 x + 6 y - 1)$

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