Find the product:
$(x + y) (2 x - 5 y + 3 x y)$ = $2 x^{2} - 3 x y + 3 x^{2} y + 3 x y^{2} - 5 y^{2}$

True

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False

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Solution

The correct option is A True
We multiply the given expressions $(x + y)$ and $(2 x - 5 y + 3 x y)$ as shown below:

$(x + y) (2 x - 5 y + 3 x y) = x (2 x - 5 y + 3 x y) + y (2 x - 5 y + 3 x y) = 2 x^{2} - 5 x y + 3 x^{2} y + 2 x y - 5 y^{2} + 3 x y^{2} = 2 x^{2} + (- 5 x y + 2 x y) + 3 x^{2} y + 3 x y^{2} - 5 y^{2} (C o m b i n i n g l i k e t e r m s) = 2 x^{2} + x y (- 5 + 2) + 3 x^{2} y + 3 x y^{2} - 5 y^{2} = 2 x^{2} - 3 x y + 3 x^{2} y + 3 x y^{2} - 5 y^{2}$

Hence, $(x + y) (2 x - 5 y + 3 x y) = 2 x^{2} - 3 x y + 3 x^{2} y + 3 x y^{2} - 5 y^{2}$ .

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