# ADD SUBTRACT AND MULTIPLY LINEAR EXPRESSIONS

Add subtract and multiply linear expressions :

Whenever we want add or subtract linear expressions, we must know about combining like terms.

Like terms or Similar terms:

Like terms are the terms which have the same variables with same exponent for each variable.

Examples : 7x, 3x, - 4x

7x and -5xy are not like terms. Because in the first term we have the variable x only. But in the second term, we have x and y.So we cannot combine them.

To add or subtract linear expression, we have two methods

(i) Horizontal method

(ii) Vertical method

Horizontal method :

In this method, we arrange all the terms in a horizontal line and then add or subtract by combining the like terms.

Vertical method :

In this method, we should write the like terms vertically and then add or subtract.

## Add subtract and multiply linear expressions - Examples

Let us look into some example problems to understand how to add subtract and multiply linear expressions.

Example 1 :

Add 6a + 3 and 4a - 2.

Solution :

Adding linear expressions in horizontal method :

=   (6a + 3) + (4a - 2)

=   6a + 4a + 3 - 2

=  10a + 1

Adding linear expressions in vertical method : Example 2 :

Add 5y + 8 + 3z and 4y - 5

Solution :

Adding linear expressions in horizontal method :

=   (5y + 8 + 3z) + (4y - 5)

=   5y + 4y + 8 - 5 + 3z

=   9y + 3z + 3

Adding linear expressions in vertical method : Example 3 :

Add 10x²- 5xy + 2y², -4x²+ 4xy + 5y², 3x²- 2xy - 6y²

Solution :

Adding linear expressions in horizontal method :

=   (10x²- 5xy + 2y²) + (-4x²+ 4xy + 5y²) + (3x²- 2xy - 6y²)

=  10x² - 4x² + 3x² - 5xy + 4xy - 2xy + 2y²+ 5y² - 6y²

=  13x² - 4x² - 7xy + 4xy + 7y² - 6y²

=  9x² - 3xy + y²

Adding linear expressions in vertical method : Example 4 :

Subtract 6a - 3b from - 8a + 9b.

Solution :

Subtracting linear expressions in horizontal method:

=   (- 8a + 9b) -  (6a - 3b)

=   - 8a + 9b -  6a + 3b

=  -8a - 6a + 9b + 3b

=  -14a + 12b

Subtracting linear expressions in vertical method : Example 5 :

Subtract a² + b² - 3ab from a² + b² - 3ab

Solution :

Subtracting linear expressions in horizontal method:

=  (a² - b² - 3ab) - (a²+ b² - 3ab)

=  a² - b² - 3ab - a² - b² + 3ab

=  a² - a² - b² - b² - 3ab  + 3ab

=  - b² - b²

=  - 2b²

Subtracting linear expressions in vertical method : Example 6 :

Multiply (3a - 2b) (2p + 3q)

Solution :

By using distributive property we can multiply two polynomials.

=  (3a - 2b) (2p + 3q)

=  3a(2p + 3q) - 2b(2p + 3q)

=  6ap + 9aq - 4pb - 6qb

Since there is not like terms, we cannot combine any more.

Hence the answer is 6ap + 9aq - 4pb - 6qb.

Example 7 :

Multiply (3x - 7) (7x - 3)

Solution :

By using distributive property we can multiply two polynomials.

=  (3x - 7) (7x - 3)

=  3x(7x - 3) - 7(7x - 3)

=  21x² - 9x - 49x + 21

=  21x² - 58x + 21

Hence the answer is  21x² - 58x + 21. After having gone through the stuff given above, we hope that the students would have understood "Add subtract and multiply linear expressions"

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