Simplify: $(4 x - 2 y) (5 x + 4 y) - (3 x^{2} + 2 y^{2})$ .

17 x^{2} + 6 x y - 10 y^{2}

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7 x^{2} - 6 x y + 10 y^{2}

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17 x^{2} - 6 x y - 7 y^{2}

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None of the above

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Solution

The correct option is A $17 x^{2} + 6 x y - 10 y^{2}$
$(4 x - 2 y) (5 x + 4 y) - (3 x^{2} + 2 y^{2}) = 4 x \times (5 x + 4 y) - 2 y \times (5 x + 4 y) - (3 x^{2} + 2 y^{2}) = 4 x \times 5 x + 4 x \times 4 y - 2 y \times 5 x - 2 y \times 4 y - 3 x^{2} - 2 y^{2} = 20 x^{2} + 16 x y - 10 x y - 8 y^{2} - 3 x^{2} - 2 y^{2} = 20 x^{2} - 3 x^{2} + 16 x y - 10 x y - 8 y^{2} - 2 y^{2} = 17 x^{2} + 6 x y - 10 y^{2}$

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