Factorise the expression $((2 a + b)^{2} - 4 (2 a + b))$ + 3.

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Solution

The given expression is $(2 a + b)^{2} - 4 (2 a + b) + 3$
Taking 2a + b = x, the expression reduces to
$x^{2} - 4 x + 3$
The product of first and last term is $3 x^{2}$
The middle term is -4x
So, two terms whose product is $3 x^{2}$ and sum is $- 4 x$ will be
$- 3 x a n d - x$
So, splitting the middle term we get,
= $x^{2} - x - 3 x + 3$
= $x (x - 1) - 3 (x - 1)$
= $(x - 3) (x - 1)$ [Taking (x-1) common]
Substituting back the value of x we get
$(2 a + b - 3) (2 a + b - 1)$

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