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.

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.

Following illustrations will illustrate these methods.

Examples on addition of algebraic expressions:

**1. 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

**Column Method:**

**Solution:**

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;

6a + 8b - 7c

- 4a + 2b + c

__ a - 3b - 2c__

__ 3a + 7b - 8c__

= 3a + 7b - 8c

**2. 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;

5x² + 7y - 8

- 2x² + 4y + 7

4x² – 5y + 6

___________

7x² + 6y + 5

___________

= 7x² + 6y + 5

**3. Add: 8x² - 5xy + 3y², 2xy - 6y² + 3x² and y² + xy - 6x².
Solution: **

Arranging the given expressions in descending powers of x with like terms under each other and adding column wise;

8x² - 5xy + 3y²

3x² - 2xy - 6y²

-6x² + xy + y²

_____________

5x² - 2xy - 2y²

_____________

= 5x² - 2xy - 2y²

**4. Add: 11a² + 8b² - 9c², 5b² + 3c² - 4a² and 3a² - 4b² - 4c².
Solution: **

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;

11a² + 8b² - 9c²

- 4a² + 5b² + 3c²

3a² - 4b² - 4c²

________________

10a² + 9b² - 10c²

________________

= 10a² + 9b² - 10c²

**5. Add the 3x + 2y and x + y.**

**Solution:**

**Horizontal Method:**

(3x + 2y) + (x + y)

Arrange the like terms together, then add.

Thus, the required addition

= 3x + 2y + x + y

= 3x + x + 2y +y

= 4x + 3y

**Column Method:**

**Solution:**

Arrange expressions in lines so that the like terms with their signs are one below the other i.e. like terms are in same vertical column and then add the different groups of like terms.

3x + 2y

+ x + y

_________

4 x + 3y

**6. Add: x + y + 3 and 3x + 2y + 5**

**Solution:**

**Horizontal Method:**

(x + y + 3) + (3x + 2y + 5)

= x + y + 3 + 3x + 2y + 5

Arrange the like terms together, then add.

Thus, the required addition

= x + 3x + y + 2y + 3 + 5

= 4x + 3y + 8

**Column Method:**

**Solution:**

Arrange expressions in lines so that the like terms with their signs are one below the other i.e. like terms are in same vertical column and then add the different groups of like terms.

x + y + 3

+ 3x + 2y + 5

_________________

4x + 3y + 8

**7. Add: 2x + 3y + z and 2x - y - z**

**Solution:**

**Horizontal Method:**

(2x + 3y + z) + (2x - y – z)

=2x + 3y + z + 2x - y – z

Arrange the like terms together, then add.

Thus, the required addition

= 2x + 2x + 3y - y + z - z

=4x + 2y

**Column Method:**

**Solution:**

Arrange expressions in lines so that the like terms with their signs are one below the other i.e. like terms are in same vertical column and then add the different groups of like terms.

2x + 3y + z

+ 2x - y - z

_____________

4x + 2y

**8. Add: 5x³ – 2y³ and 7x³ – 3y³**

**Solution:**

**Horizontal Method:**

(5x³ – 2y³) + (7x³ – 3y³)

=5x³ - 2y³ + 7x³ – 3y³

Arrange the like terms together, then add.

Thus, the required addition

= 5x³ + 7x³ - 2y³ - 3y³

=12x³ – 5y³

**Column Method:**

**Solution:**

Arrange expressions in lines so that the like terms with their signs are one below the other i.e. like terms are in same vertical column and then add the different groups of like terms.

5x³ – 2y³

+ 7x³ - 3y³

_____________

12x³ – 5y³

**9. Add: a² + b² + c² – 3abc and a² – b² + c² + abc**

**Solution:**

**Horizontal Method:**

(a² + b² + c² - 3abc) + (a² – b² + c² + abc)

= a² + b² + c² - 3abc + a² – b² + c² + abc

Arrange the like terms together, then add.

Thus, the required addition

= (a² + a²) + (b² – b²) + (c² + c²) - 3abc + abc

= 2a² + 2c² -2abc

**Column Method:**

**Solution:**

Arrange expressions in lines so that the like terms with their signs are one below the other i.e. like terms are in same vertical column and then add the different groups of like terms.

a² + b² + c² – 3abc

+ a² – b² + c² + abc

__________________

2a² + 0 + 2c² – 2abc

**10. Add: xy² + 4x²y – 7x²y - 3xy² + 3 and x²y + xy²**

We have;

xy² + 4x²y -7x²y - 3xy² + 3

= - 2xy² - 3x²y + 3

**Solution:**

**Horizontal Method:**

(xy² + 4x²y – 7x²y - 3xy² + 3) +(x²y + xy²)

= (-2xy² - 3x²y + 3) + x²y + xy²

= -2xy² - 3x²y + 3 + x²y + xy²

Arrange the like terms together, then add.

Thus, the required addition

= -2xy² + xy² - 3x²y + xy² + 3

= - xy² - 2x²y + 3

**Column Method:**

**Solution:**

Arrange expressions in lines so that the like terms with their signs are one below the other i.e. like terms are in same vertical column and then add the different groups of like terms.

- 2xy² - 3x²y +3

+ xy² + x²y

________________

- xy² - 2x²y + 3

**11. Add: 5x² + 7y - 6z², 4y + 3x², 9x² + 2z² - 9y and 2y - 2x².**

**Solution:**

**Horizontal Method:**

(5x² + 7y - 6z²) + (4y + 3x²) + (9x² + 2z² - 9y) + (2y - 2x²).

= 5x² + 7y - 6z² + 4y + 3x² + 9x² + 2z² - 9y + 2y - 2x²

Arrange the like terms together, then add.

Thus, the required addition

= 5x² + 3x² + 9x² - 2x² + 7y + 4y - 9y + 2y - 6z² + 2z²

= 15x² + 4y - 4z²

**Column Method:**

**Solution:**

Arrange expressions in lines so that the like terms with their signs are one below the other i.e. like terms are in same vertical column and then add the different groups of like terms.

5x² + 7y - 6z²

+ 3x² + 4y

+ 9x² - 9y + 2z²

- 2x² + 2y

________________

15x² + 4y - 4z².

● **Algebraic Expression****Algebraic Expression**

**Addition of Algebraic Expressions**

**Subtraction of Algebraic Expressions**

**Multiplication of Algebraic Expression**

**Division of Algebraic Expressions**

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