Find the product −3y(xy + y²) and find its value for x = 4 and y = 5.

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Solution

$- 3 y (xy + y^{2}) = - 3 y \times xy - 3 y \times y^{2} = - 3 \times x \times y \times y - 3 \times y \times y^{2} = - 3 \times x \times y^{(1 + 1)} - 3 \times y^{(1 + 2)} = - 3 {xy}^{2} - 3 y^{3} When x = 4 and y = 5, we get : L . H . S . = - 3 y (xy + y^{2}) = - 3 \times 5 (4 \times 5 + 5^{2}) = - 15 \times (20 + 25) = - 675 R . H . S . = - 3 {xy}^{2} - 3 y^{3} = - 3 \times 4 \times 5^{2} - 3 \times 5^{3} = - 300 - 375 = - 675 L . H . S . = R . H . S . ∴ - 3 y (xy + y^{2}) = - 3 {xy}^{2} - 3 y^{3}$

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Find the product $- 3 y (x y + y^{2}) and find its value for x = 4 a n d y = 5.$

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x y (x^{2} - 2 x + y^{2})

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4 x y (x - y) - 6 x^{2} (y - y^{2}) - 3 y^{2} (2 x^{2} - x) + 2 x y (x - y)

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Find the product (x $^{2}$ -3xy+2y $^{2}$ ) (2x-3y) and also find its value when x = 4 and y = -3.

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