In this section we will learn about Addition of Algebraic Expression with positive like terms and negative like terms.

Addition of Algebraic Expression Positive Like terms :

To add several positive like terms, we proceed as follows :

Step 1 : Obtain all like terms.
Step 2 : Find the sum of the numerical coefficients of all terms.
Step 3 : Write the required sum as a like term whose numerical coefficient is the numerical obtained in Step 2 and literal factor is same as the literal factors of the given like terms.

Examples:

1) Add 4xy, 12xy and 3xy.

Solution :

4xy ---> coefficient 4
12xy ----> coefficient 12
3xy -----> coefficient 3
Add all the coefficients ( 4 + 12 + 3 = 19).
Hence, 4xy + 12xy + 3xy = 19xy.

2) Add 3a2b, 2a2b, 13a2b and a2b.

Solution :

The sum of the numerical coefficient = (3 + 2 + 13 + 1 = 19)
Hence, 3a2b + 2a2b + 13a2b + a2b = 19a2b.

To add negative like terms, we proceed as follows :

Step 1 : Obtain all like terms.
Step 2 : Find the sum of the negative numerical coefficients of all terms.
Step 3 : Write an expression with numerical coefficients obtain in Step 2 and literal coefficients with negative sign in the beginning.

Examples :

1) Add -7xy, -3xy and -9xy.

Solution :

-7xy ----> coefficient -7
-3xy ----> coefficient -3
-9xy ----> coefficient -9
Add all the coefficients ( -7-3-9 = -19)
Hence,-7xy -3xy -9xy = -19xy

2) Add -4ab, -7ab,-10ab and -3ay

Solution :

The sum of numerical coefficient =(-4-7-10-3 = -24)
Hence, -4ab-7ab-10ab-3ab = -24ab.

Addition of Algebraic Expressions with Like and Unlike terms

In adding algebraic expressions containing like and unlike terms, we collect different groups of like terms and find the sum of like terms in each group bye the methods discussed above.

Examples :

1) 7x +4 and 3x -1
= (7x + 4) + (3x -1)
= 7x + 4 + 3x -1 [ Marking of like terms]
= 10x + 3
2) a2 + b2 + c2 – 3abc and a2 – b2 + c2 + abc
= (a2 + b2 + c2 – 3abc) + (a2 – b2 + c2 + abc)
= a2 + b2 + c2 – 3abc + a2 – b2 + c2 + abc
= a2 + b2 + c2 - 3abc + a2 -b2 + c2 + abc [ Marking of like terms]
= 2a2 + 0 + 2c2 - 2abc
= 2a2 + 2c2 - 2abc

Algebraic Expressions

Like and Unlike terms in Algebra