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Addition of Algebraic Expression

Introduction to Algebra II - Concepts

Finding Value of an Expression

Addition of Algebraic Expression

Subtraction of Algebraic Expression

Multiplication of Monomials

Multiplication of Binomials

Multiplication of Binomial with a Monomial

Division of Polynomial by a Monomial

Class - Sainik School Entrance 6th Subjects

Concept Explanation

Addition of Algebraic Expression

In addition of algebraic expressions while adding algebraic expressions we collect the like terms and add them. The sum of several like terms is the like term whose coefficient is the sum of the coefficients of these like terms.

To add two or more monomials that are like terms, add the coefficients; keep the variables and exponents on the variables the same.

When we add two algebraic expressions, the like term are added, the unlike terms are left as they are. Hence the sum of like terms 5x and 2x add to 7x.

Illustration: Simplify 13x + 7y − 2x + 6a

Solution: 13x + 7y − 2x + 6a

The only like terms in this expression are13x and −2x. We cannot do anything with the 7y or 6a.

So we group together the terms we can subtract, and just leave the rest:

(13x − 2x) + 6a + 7y

= 6a + 11x + 7y

NOTE : Two ways to solve addition of algebraic expressions.

Horizontal Method:

In this method, all expressions are written in a horizontal line and then the terms are arranged to collect all the groups of like terms and then added.

Column Method:

In this method each expression is written in a separate row such that there like terms are arranged one below the other in a column. Then the addition of terms is done column wise. Examples on addition of algebraic expressions:

Illustration: Add: 6a + 8b - 7c, 2b + c - 4a and a - 3b - 2c

Solution Horizontal Method:

(6a + 8b - 7c) + (2b + c - 4a) + (a - 3b - 2c)

= 6a + 8b - 7c + 2b + c - 4a + a - 3b - 2c

Arrange the like terms together, then add. Thus, the required addition

= 6a - 4a + a + 8b + 2b - 3b - 7c + c - 2c

= 3a + 7b - 8c

Solution Column Method: Writing the terms of the given expressions in the same order in form of rows with like terms below each other and adding column wise;

Illustration. Add: 5x² + 7y - 8, 4y + 7 - 2x² and 6 – 5y + 4x².

Solution: Writing the given expressions in descending powers of x in the form of rows with like terms below each other and adding column wise;

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Simplify : $large 5x+3x$ =
A. 6x	B. 5x	C. 8x	D. 9x
Right Option : C
View Explanation

Question : 2

Add: -7mn + 5, 12mn + 2, 9mn - 8, -2mn -3
A. 13mn - 2	B. 15mn - 7	C. 12mn - 4	D. 13mn - 4
Right Option : C
View Explanation

Question : 3

Simplify the following : 3 $a^{2}$ + 2ab - 5 $b^{2}$ , -7 $a^{2}$ - 10 $b^{2}$ - 5ab, 30 $a^{2}$ + 10 $b^{2}$
A. 26 $a^{2}$ - 3ab - 5 $b^{2}$	B. 28 $a^{2}$ - 3ab - 5 $b^{2}$	C. 26 $a^{2}$ - 3ab - 9 $b^{2}$	D. 26 $a^{2}$ - 3ab - 7 $b^{2}$
Right Option : A
View Explanation