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Algebraic Identities

Expand 2a+3...

Question

Expand ${(2 a + 3)}^{2}$ using appropriate identity

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Solution

We know that the identity: $(x + y)^{2} = x^{2} + y^{2} + 2 x y$ .

Consider $(2 a + 3)^{2}$ and apply the above identity as follows:
Taking $x = 2 a$ and $y = 3$ in the above identity.
We get, $(2 a + 3)^{2} = 2 a^{2} + 3^{2} + (2 \times 2 a \times 3) = 4 a^{2} + 9 + 12 a$
Hence, $(2 a + 3)^{2} = 4 a^{2} + 12 a + 9$ .

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