Factorise: $(5 a - 2 b)^{2} - (2 a - b)^{2}$ .

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Solution

Using the formula: $x^{2} - y^{2} = (x + y) (x - y)$

Substituing, $x = 5 a - 2 b$ and $y = 2 a - b$ in the above fomula we get:

$(5 a - 2 b)^{2} - (2 a - b)^{2} = [(5 a - 2 b) + (2 a - b)] [(5 a - 2 b) - (2 a - b)]$
$= (7 a - 3 b) (3 a - b)$ ,

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