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