R. D. Sharma Solutions for Chapter: Algebraic Expressions, Exercise 2: EXERCISE

Add the following expressions:
${\mathrm{x}}^3-2{\mathrm{x}}^2\mathrm{y}+3{\mathrm{xy}}^2-{\mathrm{y}}^3,$ $2{\mathrm{x}}^3-5{\mathrm{xy}}^2+3{\mathrm{x}}^2\mathrm{y}-4{\mathrm{y}}^3$

Add the following expressions:
${\mathrm{a}}^4-2{\mathrm{a}}^3\mathrm{b}+3{\mathrm{ab}}^3+4{\mathrm{a}}^2{\mathrm{b}}^2+3{\mathrm{b}}^4,$ $-2{\mathrm{a}}^4-5{\mathrm{ab}}^3+7{\mathrm{a}}^3\mathrm{b}-6{\mathrm{a}}^2{\mathrm{b}}^2+{\mathrm{b}}^4$

Add the following expressions:
$5{\mathrm{x}}^3+7+6\mathrm{x}-5{\mathrm{x}}^2, 2{\mathrm{x}}^2-8-9\mathrm{x}, 4\mathrm{x}-2{\mathrm{x}}^2+3{\mathrm{x}}^3, 3{\mathrm{x}}^3-9\mathrm{x}-{\mathrm{x}}^2$ and $\mathrm{x}-{\mathrm{x}}^2-{\mathrm{x}}^3-4$

Add $2{\mathrm{x}}^2-3\mathrm{x}+1$ to the sum of $3{\mathrm{x}}^2-2\mathrm{x}$ and $3\mathrm{x}+7$.

Add ${\mathrm{x}}^2+2\mathrm{xy}+{\mathrm{y}}^2$ to the sum of ${\mathrm{x}}^2-3{\mathrm{y}}^2$ and $2{\mathrm{x}}^2-{\mathrm{y}}^2+9$.

Add ${\mathrm{a}}^3+{\mathrm{b}}^3-3$ to the sum of $2{\mathrm{a}}^3-3{\mathrm{b}}^3-3\mathrm{ab}+7$ and $-{\mathrm{a}}^3+{\mathrm{b}}^3+3\mathrm{ab}-9$.

From ${\mathrm{x}}^3-5{\mathrm{x}}^2+3\mathrm{x}+1$, take away $6{\mathrm{x}}^2-4{\mathrm{x}}^3+5+3\mathrm{x}$.

From the sum of $3x^2-5x+2$ and $-5x^2-8x+9$ subtract $4x^2-7x+9$.