Factorise:

Question:

Factorise:

$25 x^{2}-10 x+1-36 y^{2}$

 

Solution:

$25 x^{2}-10 x+1-36 y^{2}$

$=\left[(5 x)^{2}-2 \times 5 x \times 1+1^{2}\right]-(6 y)^{2}$

$=(5 x-1)^{2}-(6 y)^{2} \quad\left[a^{2}-2 a b+b^{2}=(a-b)^{2}\right]$

$=[(5 x-1+6 y)][(5 x-1-6 y)] \quad\left[a^{2}-b^{2}=(a+b)(a-b)\right]$

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

 

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