Find the product of $(3 x - 2 y)$ and $(3 x + 4 y)$ .

9 x^{2} + 8 y^{2}

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9 x^{2} + 12 x y - 8 y^{2}

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9 x^{2} + 6 x y - 8 y^{2}

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None of the above

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Solution

The correct option is C $9 x^{2} + 6 x y - 8 y^{2}$
$(3 x - 2 y) \times (3 x + 4 y) = 3 x \times (3 x + 4 y) - 2 y \times (3 x + 4 y)$ (using distributive property) $= 9 x^{2} + 12 x y - 6 x y - 8 y^{2} = 9 x^{2} + 6 x y - 8 y^{2}$

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Simplify: $(3 x - 2 y) (3 x + 4 y) - (3 x + 2 y) (3 x - 2 y)$

4 y = 3 x^{2}

2 y = 3 x + 12

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