Find the following product and verify the result for x = − 1, y = − 2:
(3x − 5y) (x + y)

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Solution

To multiply, we will use distributive law as follows:

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

$∴$ $(3 x - 5 y) (x + y) = 3 x^{2} - 2 x y - 5 y^{2}$ .
Now, we put x = $-$ 1 and y = $-$ 2 on both sides to verify the result.

$LHS = (3 x - 5 y) (x + y) = \{3 (- 1) - 5 (- 2)\} \{- 1 + (- 2)\} = (- 3 + 10) (- 3) = (7) (- 3) = - 21$

$RHS = 3 x^{2} - 2 x y - 5 y^{2} = 3 {(- 1)}^{2} - 2 (- 1) (- 2) - 5 {(- 2)}^{2} = 3 \times 1 - 4 - 5 \times 4 = 3 - 4 - 20 = - 21$

Because LHS is equal to RHS, the result is verified.

Thus, the answer is $3 x^{2} - 2 x y - 5 y^{2}$ .

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