Question 60 (a)

What should be subtracted from $2 x^{3} - 3 x^{2} y + 2 x y^{2} + 3 y^{3}$ to get $x^{3} - 2 x^{2} y + 3 x y^{2} + 4 y^{3} ?$

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Solution

In order to get the solution, we will subtract $x^{3} - 2 x^{2} y + 3 x y^{2} + 4 y^{3}$ from $2 x^{3} - 3 x^{2} y + 2 x y^{2} + 3 y^{3} .$
Required expression is
$2 x^{3} - 3 x^{2} y + 2 x y^{2} + 3 y^{3} - (x^{3} - 2 x^{2} y + 3 x y^{2} + 4 y^{3}) = 2 x^{3} - 3 x^{2} y + 2 x y^{2} + 3 y^{3} - x^{3} + 2 x^{2} y - 3 x y^{2} - 4 y^{3}$
On combining the like terms.
$= 2 x^{3} - x^{3} - 3 x^{2} y + 2 x^{2} y + 2 x y^{2} - 3 x y^{2} + 3 y^{3} - 4 y^{3} = x^{3} - x^{2} y - x y^{2} - y^{3}$
So, if we subtract $x^{3} - x^{2} y - x y^{2} - y^{3}$ from $2 x^{3} - 3 x^{2} y + 2 x y^{2} + 3 y^{3}$ . then we get $x^{3} - 2 x^{2} y + 3 x y^{2} + 4 y^{3}$ .

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Question 59 (a)

What should be added to $x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3}$ to get $x^{3} + y^{3} ?$

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

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

8 x^{2} y

x^{3} - 3 x^{2} + 5 x - 1

2 x^{3} + x^{2} - 4 x + 2

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