Expand ${(3 x + 4 y)}^{2}$

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Solution

${(3 x + 4 y)}^{2}$ is the product of two binomial expressons, which have the same terms $(3 x + 4 y)$ and $(3 x + 4 y)$ . It can be expanded by the method of multiplying a binomial by a binomial.
On Comparing the identities with this product. In this product $a = 3 x$ and $b = 4 y$ . We can get the result of this product by substituting $3 x$ and $4 y$ terms in the place of $a$ and $b$ respectively in the first identity ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$
Hence, ${(3 x + 4 y)}^{2} = {(3 x)}^{2} + 2 (3 x) (4 y) + 4 y^{2}$
$= 9 x^{2} + 24 x y + 16 y^{2}$

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