Question 57 (b)

Add the following expression:

$x^{3} - x^{2} y - x y^{2} - y^{3}$ and $x^{3} - 2 x^{2} y + 3 x y^{2} + 4 y$

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Solution

We have, $x^{3} - x^{2} y - x y^{2} - y^{3}$ and $x^{3} - 2 x^{2} y + 3 x y^{2} + 4 y$
On combining the like terms,
$= x^{3} + x^{3} - x^{2} y - 2 x^{2} y - x y^{2} + 3 x y^{2} - y^{3} + 4 y = 2 x^{3} - 3 x^{2} y + 2 x y^{2} - y^{3} + 4 y$

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Question 58 (c)

Subtract:

$- 4 x^{2} y - y^{3}$ from $x^{3} + 3 x y^{2} - x^{2} y .$

x^{3} - x^{2} y + 5 x y^{2} + y^{3}; - x^{3} + y^{3} - 9 x y^{2} and 3 x y^{2} + 9 x^{2} y .

x^{3} - y^{3} = 127, x^{2} y - x y^{2} = 42

x^{3} + x^{2} y - x y^{2} = y^{3}

\frac{d y}{d x}

x^{3} + x^{2} y + x y^{2} + y^{3} = 81

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