Find the following products and verify the result for x = -1, y = - 2:

$(3 x - 5 y) (x + y)$

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Solution

$(3 x - 5 y) (x + y) = 3 x \times (x + y) - 5 y \times (x + y) = 3 x \times x + 3 x \times y - 5 y \times x - 5 y \times y = 3 x^{2} + 3 x y - 5 x y - 5 y^{2} = 3 x^{2} - 2 x y - 5 y^{2} Verification x = - 1, y = - 2 L . H . S = (3 x - 5 y) (x + y) = [3 (- 1) - 5 (- 2)] [- 1 - 2] = (- 3 + 10) (- 3) = 7 \times (- 3) = - 21 R . H . S . = 3 x^{2} - 2 x y - 5 y^{2} = 3 (- 1)^{2} - 2 (- 1) (- 2) - 5 (- 2)^{2} = 3 \times 1 - 4 - 5 \times 4 = 3 - 4 - 20 = 3 - 24 = - 21 ∴ L . H . S . = R . H . S .$

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