**Objective**

To add two algebraic expressions (polynomials).

##

**Theory**

## Polynomial

- Polynomials are algebraic expressions that consist of constants and variables of different powers.
- Adding polynomials is a way of combining and summing up terms having the same power.

### Addition of Polynomials

Adding polynomials is defined as the addition operation of polynomials. While adding polynomials we follow some specific rules which makes it very simple to do the operation.

__Like Terms__

In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. For e.g 2x+9x, 3w-87w etc.

__Unlike Terms__

Algebraic terms, which does not have the same literal coefficients, and cannot be raised to the same power are called, unlike terms. For e.g 23x+7w², 65x²-4q

### Rules of Adding Polynomials:-

- Rule 1: The like terms are always combined and added. Unlike terms can never be added.
- Rule 2: While adding the terms, the sign always remains the same.

Add the Algebraic expression using Horizontal Method:-

- Step 1: Write all addends in line with addition signs in between.
- Step 2: As the sign before the bracket is +, the common multiplier is +1. So, remove the brackets without changing the sign of the terms.
- Step 3: Group the like terms together.
- Step 4: Add the like terms to obtain the sum of expressions.

Add the Algebraic expression using Vertical Method:-

- Step 1: Write the polynomials in standard form.
- Step 2: Place the polynomials in a vertical arrangement, with the like terms placed one above the other in both the polynomials.
- Step 3: If any power term is missing in any polynomial, we write a '0' as its coefficient to avoid confusion in the column-wise arrangement.
- Step 4: Perform the calculations by retaining the sign of the terms.