Addition and Subtraction of Algebraic Expressions

If $A=x+y$ and $B=x-y$, then find $A+B$

$\left(p^2+3m^2+2n^2\right)+\left(-2p^2+4m^2-5n^2\right)$ is :

Find the sum of $3{\mathrm{x}}^2\mathrm{y}+2{\mathrm{xy}}^2$ and$5{\mathrm{xy}}^2-8{\mathrm{x}}^2\mathrm{y}+3\mathrm{xy}$.

A rectangle has a length of ${\mathrm{x}}^2+4{\mathrm{y}}^{3 }$and a breadth of $-2{\mathrm{x}}^2+{\mathrm{y}}^3$. What is its perimeter ?

A Triangle has sides $\mathrm{x}+1, 3\mathrm{x}+6\mathrm{y}+2 \mathrm{and} \mathrm{x}-\mathrm{y}-9.$ Find its perimeter.

How much less is $7{\mathrm{a}}^2+9{\mathrm{b}}^2-21\mathrm{ab} \mathrm{than} {\mathrm{a}}^2-{\mathrm{b}}^2+2\mathrm{ab}$?

Subtract${\mathrm{a}}^2+3{\mathrm{b}}^2 \mathrm{from} -5{\mathrm{b}}^2+8{\mathrm{c}}^2$.

Add the following polynomials:

${\mathrm{q}}^3+2\mathrm{q}, 5\mathrm{q} \mathrm{and} 4-2{\mathrm{q}}^3$

Add the following polynomials:

$5{\mathrm{x}}^2+4\mathrm{x}+3, 15{\mathrm{x}}^2-3\mathrm{x}+8 \mathrm{and} 6{\mathrm{x}}^2-\mathrm{x}+9$

Subtract the following:

$3{\mathrm{m}}^2-2+11\mathrm{m} \mathrm{from} {\mathrm{m}}^3-9$

Subtract the following:

$4{\mathrm{z}}^2\mathrm{xy}+{\mathrm{x}}^2\mathrm{zy}-5\mathrm{xyz}+2{\mathrm{xy}}^2\mathrm{z} \mathrm{from} {\mathrm{x}}^2\mathrm{zy}+\mathrm{xyz}+{\mathrm{xy}}^2\mathrm{z}-{\mathrm{z}}^2\mathrm{xy}$

Subtract the following:

$3\mathrm{r}+2\mathrm{t} \mathrm{from} 2\mathrm{r}-3\mathrm{t}$

What should be added to $\frac{4}{3}{\mathrm{x}}^3\mathrm{z}+{\mathrm{xz}}^3$ to make it $\frac{1}{10}{\mathrm{x}}^3\mathrm{z}+6{\mathrm{xz}}^3$?

Perform the following subtraction.

Subtract $\mathrm{m}-8$ from $1-\mathrm{m}+\mathrm{n}$.

Add the following expressions,

 $-{\mathrm{x}}^3+7\mathrm{x}-23, 5{\mathrm{x}}^3-11\mathrm{x}$ and $49.$

Add the following expressions:

 $3\mathrm{ab}+2{\mathrm{a}}^2{\mathrm{b}}^2, -\mathrm{ab}-{\mathrm{a}}^2{\mathrm{b}}^2$ and $10\mathrm{ab}+15{\mathrm{a}}^2{\mathrm{b}}^2$.

Add the following.

(a) $3{\mathrm{a}}^2,-5{\mathrm{a}}^2,7{\mathrm{a}}^2$ 

(b) $6\mathrm{pq},-8\mathrm{pq},9\mathrm{pq}$