Factorise the following: $4 x^{2} + 12 x y + 5 y^{2}$

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Solution

Given: $4 x^{2} + 12 x y + 5 y^{2}$
$= 4 x^{2} + 2 x y + 10 x y + 5 y^{2}$ ,( split the middle term so that resultant is same)
$= (4 x^{2} + 2 x y) + (10 x y + 5 y^{2})$ , (group pair of terms)
$= 2 x (2 x + y) + 5 (2 x + y)$ , (factor each binomials)
$= (2 x + y) (2 x + 5 y)$ , (factor out common factor $(2 x + y)$ )

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