$(\frac{1}{5} x + 2 y) (\frac{2}{3} x - y) =$

2 x^{2} - 30 x y + 17 y^{2}

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\frac{2 x^{2} - 30 y^{2} + 17 x y}{15}

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2 x^{2} - 30 y^{2} + 17 x y

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Solution

The correct option is B $\frac{2 x^{2} - 30 y^{2} + 17 x y}{15}$
Let us solve the given expression as follows:

$(\frac{1}{5} x + 2 y) (\frac{2}{3} x - y) = (\frac{1}{5} x + \frac{2 \times 5}{1 \times 5} y) (\frac{2}{3} x - \frac{1 \times 3}{1 \times 3} y) (T a k i n g L C M) = (\frac{1}{5} x + \frac{10}{5} y) (\frac{2}{3} x - \frac{3}{3} y) = (\frac{x + 10 y}{5}) (\frac{2 x - 3 y}{3}) = \frac{1}{15} (x + 10 y) (2 x - 3 y) = \frac{1}{15} ({2 x}^{2} - 3 x y + 20 x y - 30 y^{2}) = \frac{{2 x}^{2} - 30 y^{2} + 17 x y}{15}$

Hence, $(\frac{1}{5} x + 2 y) (\frac{2}{3} x - y) = \frac{{2 x}^{2} - 30 y^{2} + 17 x y}{15}$

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$3 x^{3} + 2 x^{2} + 3 x + 2$ =?

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