# Addition of Algebraic Expression

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 3a

^{2}b, 2a

^{2}b, 13a

^{2}b and a

^{2}b.

**Solution :**

The sum of the numerical coefficient = (3 + 2 + 13 + 1 = 19)

Hence, 3a

^{2}b + 2a

^{2}b + 13a

^{2}b + a

^{2}b = 19a

^{2}b.

**Addition of Negative Like terms**

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 :**

**Add the following :**

**1) 7x +4 and 3x -1**

= (7x + 4) + (3x -1)

=

= 10x + 3

2) a

= (a

= a

= a

= 2a

= 2a

= (7x + 4) + (3x -1)

=

__7x__+ 4 +__3x__-1 [ Marking of like terms]= 10x + 3

2) a

^{2}+ b^{2}+ c^{2}– 3abc and a^{2}– b^{2}+ c^{2}+ abc= (a

^{2}+ b^{2}+ c^{2}– 3abc) + (a^{2}– b^{2}+ c^{2}+ abc)= a

^{2}+ b^{2}+ c^{2}– 3abc + a^{2}– b^{2}+ c^{2}+ abc= a

^{2}__+ b__^{2}+ c^{2}- 3abc + a^{2}__-b__^{2}+ c^{2}+ abc [ Marking of like terms]= 2a

^{2}+ 0 + 2c^{2}- 2abc= 2a

^{2}+ 2c^{2}- 2abc**Algebraic Expressions**

• Like and Unlike terms in Algebra

• Addition of algebraic expressions

• Subtraction of algebraic expressions

• Multiplication of algebraic expressions

• Division of algebraic expressions

• Like and Unlike terms in Algebra

• Addition of algebraic expressions

• Subtraction of algebraic expressions

• Multiplication of algebraic expressions

• Division of algebraic expressions