Find the value of $(3 p + 2 a)^{2}$

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Solution

We need to factorise $(3 p + 2 a)^{2}$
We know the identity $(x + y)^{2} = x^{2} + y^{2} + 2 x y$
Here $x = 3 p, y = 2 a$
Thus we can solve it as $(3 p + 2 a)^{2} = (3 p)^{2} + 2 \times 3 p \times 2 a + (2 a)^{2}$
$= 9 p^{2} + 4 a^{2} + 12 p a$

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