Evaluate the product of $(2 x - 3 y)$ and $(x - y)$ .

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Solution

The given polynomials are $2 x - 3 y$ and $x - y$ .
We multiply them as follows:
$(2 x - 3 y) (x - y)$
$= (2 x \times x) + (2 x \times - y) + (- 3 y \times x) + (- 3 y \times - y)$
$= 2 x^{2} - 2 x y - 3 x y + 3 y^{2}$
$= 2 x^{2} - 5 x y + 3 y^{2}$

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

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