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.