Expansion of (2x + 3y)^2.We use the identity (a+b)^2 = a^2 + 2ab + b^2So, here a=2x and b=3y⇒ (2x + 3y)^2 = (2x)^2 + 2× 2x× 3y + (3y)^20ex0ex ...

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Algebraic Identities

Expand 2x + 3...

Question

Expand ${(2 x + 3 y)}^{2}$ .

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Solution

Expansion of ${(2 x + 3 y)}^{2}$ .
We use the identity ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$
So, here $a = 2 x and b = 3 y$
${\Rightarrow (2 x + 3 y)}^{2} = (2 x)^{2} + 2 \times 2 x \times 3 y + {(3 y)}^{2} = 4 x^{2} + 12 x y + 9 y^{2}$
Hence, expansion of ${(2 x + 3 y)}^{2}$ is $4 x^{2} + 12 x y + 9 y^{2}$ .

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