Multiply the binomials:
$x - 2 y$ and $2 x - y$ = $2 x^{2} - x y + 2 y^{2}$

True

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False

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Solution

The correct option is B False
We multiply the given binomials $(x - 2 y)$ and $(2 x - y)$ as shown below:

$(x - 2 y) (2 x - y) = x (2 x - y) - 2 y (2 x - y) = 2 x^{2} - x y - 4 x y + 2 y^{2} = 2 x^{2} + (- x y - 4 x y) + 2 y^{2} (C o m b i n i n g l i k e t e r m s) = 2 x^{2} - x y (1 + 4) + 2 y^{2} = 2 x^{2} - 5 x y + 2 y^{2}$

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

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