Question:
Factorise:
$25 x^{2}-10 x+1-36 y^{2}$
Solution:
$25 x^{2}-10 x+1-36 y^{2}$
$=\left[(5 x)^{2}-2 \times 5 x \times 1+1^{2}\right]-(6 y)^{2}$
$=(5 x-1)^{2}-(6 y)^{2} \quad\left[a^{2}-2 a b+b^{2}=(a-b)^{2}\right]$
$=[(5 x-1+6 y)][(5 x-1-6 y)] \quad\left[a^{2}-b^{2}=(a+b)(a-b)\right]$
$=(5 x+6 y-1)(5 x-6 y-1)$