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Question
Factorize each of the following algebraic expression:
25x2 − 10x + 1 − 36y2
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Solution
\[25 x^2 - 10x + 1 - 36 y^2 \]
\[ = (25 x^2 - 10x + 1) - 36 y^2 \]
\[ = [(5x )^2 - 2 \times 5x \times 1 + 1] - 36 y^2 \]
\[ = (5x - 1 )^2 - (6y )^2 \]
\[ = [(5x - 1) - 6y][(5x - 1) + 6y]\]
\[ = (5x - 1 - 6y)(5x - 1 + 6y)\]
\[ = (5x - 6y - 1)(5x + 6y - 1)\]
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