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Simplifying Expressions

In this worksheet, students simplify algebraic expressions.

'Simplifying Expressions' worksheet

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Simplify Algebraic Expressions to Maintain Equivalence

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

In this worksheet, we will learn how to simplify expressions.

 

To simplify an expression we have to collect together the terms that are alike, that is all the x's, all the y's and all the terms that are just numbers.

Sometimes it is necessary to multiply out brackets.    

Remember we are just simplifying expressions.  It is impossible to solve expressions as there are no equals signs and these are not equations.

 

Example 1

Simplify 2x + 5 - 4x - 1 + x

 

Answer 1

2x - 4x + x + 5 - 1

= -x + 4 or 4 - x

 

Example 2

Simplify 3(x - 4) - 2(x - 1)

 

Answer 2

First, we multiply out the brackets to get

3x - 12 - 2x + 2

Then we collect like terms.

3x - 2x - 12 + 2

x - 10

Which is the correct simplification of the expression?

 

4y - 2x + 8y + 4x

2y + 12x

12y+2x

13y + 3x

12y + 6x

Can you simplify the expression below?

 

8x + 9 - 4x - 5 + x

2y + 12x

12y+2x

13y + 3x

12y + 6x

Simplify the expression:

 

7(x - 2) - 5

2y + 12x

12y+2x

13y + 3x

12y + 6x

Simplify the expression:

 

5(x + 7) - 4(x - 4)

 

x + 19

x + 51

19 + x

51 + x

Simplify the expression:

 

7x + 2 - 3x - 8 + x

-6 + 5x

11x +10

5x - 6

4x - 6

Simplify the expression:

 

7y - 4x + 4y + 7x

 

11x + 11y

11y + 3x

11x - 3y

Simplify the expression:

 

4x + 9 - 8x - 3 + x

 

13x + 6

-4x - 12

6 - 3x

Simplify the expression:

 

4y - 9x + 6y + 2x

-7x + 10y

-2y + 11x

-2y - 11x

Simplify the expression:

 

2(x - 9) - 2

2x - 11

2x - 16

2x - 20

Simplify the expression:

 

4 (x - 6) - 3

4x - 21

4x - 27

4x + 21

  • Question 1

Which is the correct simplification of the expression?

 

4y - 2x + 8y + 4x

CORRECT ANSWER
12y+2x
EDDIE SAYS
Ok, how did you get on? Did you remember where to start? With this type of question, we need to collect like terms together. In this case, we have: 4y + 8y and -2x + 4x So, now we simplify: 4y + 8y = 12y -2x + 4x = 2x So, our simplified equation is: 12y + 2x Let's try another one!
  • Question 2

Can you simplify the expression below?

 

8x + 9 - 4x - 5 + x

CORRECT ANSWER
EDDIE SAYS
We need to always remember to start by collecting like terms together. In this case, we have: 8x - 4x + x and 9 - 5 So, now we simplify: 8x - 4x + x= 5x 9 - 5 = 4 So, our simplified equation is: 5x - 4 Did you follow this?
  • Question 3

Simplify the expression:

 

7(x - 2) - 5

CORRECT ANSWER
EDDIE SAYS
This one looked a bit different, but if we apply the rules of BODMAS we will be fine! We must, first of all, think about the brackets, we can't complete the sum in them so we now multiply the bracket by 7 to get... 7x -14 (don't forget the minus sign, it is very important) Now, we apply the last part of the sum: 7x-14 -5 = 19 Did you get that? Remember, just think about the maths rules you know as you complete these activities and take your time!
  • Question 4

Simplify the expression:

 

5(x + 7) - 4(x - 4)

 

CORRECT ANSWER
x + 51
51 + x
EDDIE SAYS
Did you see what you had to do here? First, we need to solve each bracket and then we can simplify. 5 (x + 7) = 5x + 35 - 4 (x - 4) = -4x + 16 (remember a minus multiplied by a minus results in a positive number) Now we can simplify. 5x - 4x = x 35+ 16 = 51 So, our answer is x + 51
  • Question 5

Simplify the expression:

 

7x + 2 - 3x - 8 + x

CORRECT ANSWER
-6 + 5x
5x - 6
EDDIE SAYS
Can you remember what to do? We need to collect the like terms and then simplify the equation. First, we collect the x terms and simplify: 7x - 3x + x = 5x Now, we can collect the numerical terms and simplify: 2 - 8 = -6 When we put it all together we have 5x - 6. How did you get on?
  • Question 6

Simplify the expression:

 

7y - 4x + 4y + 7x

 

CORRECT ANSWER
11y + 3x
EDDIE SAYS
You know the system now! Let's collect those like terms! 7y + 4y = 11y -4x + 7x = 3x When we put it all together we have 11y + 3x
  • Question 7

Simplify the expression:

 

4x + 9 - 8x - 3 + x

 

CORRECT ANSWER
6 - 3x
EDDIE SAYS
Step 1 - collect the like terms! 4x - 8x + x = -3x 9 - 3 = 6 So simplified we have -3x +6, but you may see the answer is the other way around 6 -3x. It doesn't matter which way around you have it as long as you use the correct sign in front of each term.
  • Question 8

Simplify the expression:

 

4y - 9x + 6y + 2x

CORRECT ANSWER
-7x + 10y
EDDIE SAYS
Are you feeling confident with this now? 4y + 6y = 10y -9x + 2x = -7x Let's put it together... 10y -7x OR -7x + 10y
  • Question 9

Simplify the expression:

 

2(x - 9) - 2

CORRECT ANSWER
2x - 20
EDDIE SAYS
Did you get it? First, we need to expand the bracket and then collect like terms and simplify. When we expand the bracket we get: 2x - 18 - 2 This gives us: 2x -20
  • Question 10

Simplify the expression:

 

4 (x - 6) - 3

CORRECT ANSWER
4x - 27
EDDIE SAYS
Last question coming up! First, we expand the bracket. 4x - 24 - 3 Which gives us 4x - 27. Great work! That's another activity completed, well done! Why not try another activity to really test your understanding.
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