Expand:
${((\frac{3}{4}) x + (\frac{2}{9}) y)}^{2}$

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Solution

Given that ${((\frac{3}{4}) x + (\frac{2}{9}) y)}^{2}$
According to the identify $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ we have to expand the given expression
${((\frac{3}{4}) x + (\frac{2}{9}) y)}^{2} = {((\frac{3}{4}) x)}^{2} + 2 ((\frac{3}{4}) x) \times ((\frac{2}{9}) y) + {((\frac{2}{9}) y)}^{2}$
$∴ {((\frac{3}{4}) x + (\frac{2}{9}) y)}^{2} = (\frac{9}{16}) x^{2} + (\frac{1}{3}) x y + (\frac{4}{81}) y^{2}$
$∴ {((\frac{3}{4}) x + (\frac{2}{9}) y)}^{2} = (\frac{9}{16}) x^{2} + (\frac{1}{3}) x y + (\frac{4}{81}) y^{2}$

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