ADD SUBTRACT AND MULTIPLY LINEAR EXPRESSIONS WORKSHEET

About "Add subtract and multiply linear expressions worksheet"

Add subtract and multiply linear expressions worksheet :

You can find some practice questions on add, subtract and multiply linear expressions.

Add subtract and multiply linear expressions - Questions 

(1)  Add 6a + 3 and 4a - 2

(2)  Add 5y + 8 + 3z and 4y - 5

(3)  Subtract 6a - 3b from - 8a + 9b

(4)  Subtract a² + b² - 3ab from a² + b² - 3ab

(5)  Multiply (3a - 2b) (2p + 3q)

(6)  Multiply (3x - 7) (7x - 3)

Add subtract and multiply linear expressions worksheet - Solution

Question 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 :

Question 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 :

Question 4 :

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

Solution : 

Subtracting linear expressions in horizontal method: 

  =   (- 8a + 9b) -  (6a - 3b)

Distribute the negative sign inside the parentheses 

  =   - 8a + 9b -  6a + 3b

=  -8a - 6a + 9b + 3b

=  -14a + 12b

Subtracting linear expressions in vertical method :

Question 4 :

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 :

Question 5 :

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.

Question 6 :

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.

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