Factorise $25 a^{2} + 40 a b + 16 b^{2}$

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Solution

Here you can see that
$25 a^{2} + 40 a b + 16 b^{2} = (5 a)^{2} + 2 (5 a) (4 b) + (4 b)^{2}$
Comparing this expression with $x^{2} + 2 x y + y^{2}$ ,
we observe that $x = 5 a$ and $y = 4 b$
Using Identity I, $(x + y)^{2} \equiv x^{2} + 2 x y + y^{2}$ , we get
$25 a^{2} + 40 a b + 16 b^{2}$
$= (5 a + 4 b)^{2}$
$= (5 a + 4 b) (5 a + 4 b)$ .

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