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Simplify Terms with Brackets

In this worksheet, students will simplify terms with brackets using index laws.

'Simplify Terms with Brackets' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Algebra

Curriculum subtopic:   Notation, Vocabulary and Manipulation, Algebraic Expressions

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

You probably know how to expand simple bracket such as: 5(b + 3) = 5b + 15 or 5a(b + 4) = 5ab + 20a.

Now we are going to look at expanding brackets where some of the terms involve indices.

 

You can use index laws to help you simplify terms when expanding brackets.

Remember that when you multiply out the numbers with indices, you just add the powers.

For example w³ × w² = w5

 

Let's apply this to expanding brackets.

Expand 5a²(a4 + 2a)

5a² × a4 = 5a6

5a² × 2a = 10a³

So the answer is 5a6 + 10a³.

Expand 3a3(a5 - 3a)

.3a15 - 9a3

3a8 - 9a4

.3a8 + 9a4

.3a8 - 3a4

Match the expressions with brackets to the correct expanded versions.

Column A

Column B

x(x² + 2)
3x5 + 6x
3x(x² + 2)
3x³ + 6x
3x3(x² + 2)
x³ + 2x
3x3(5x² + 2)
15x5 + 6x3

Expand this bracket: 2y³(2y4 - 3y)

2y7 - 2y4

2y7 - 3y4

4y12 - 6y3

4y7 - 6y4

Which of these will expand to give 36x8 - 12x5?

6x5(6x3 - 2)

6x5(6x3 - 2)

4x2(9x6 - 3x3)

9x4(4x2 - 3x)

Spot the mistake!

Underline the part of the expression which has been expanded incorrectly.

7x3(3x² + 2x) = 21x6 + 14x4

21x6 + 14x4

Expand 5x⊃(2x² + 3x4 - x³).

10x4 + 15x8 - 5x6

10x4 + 15x6 - 5x5

7x4 + 8x6 - 4x5

7x4 + 8x8 - 4x6

Match the brackets to the correct expansions.

Column A

Column B

2x²(3x³ + 4x4 + 5x5
9x5 + 12x6 + 15x7
3x²(3x³ + 4x4 + 5x5
12x5 + 15x6 + 18x7
2x²(4x³ + 5x4 + 6x5
8x5 + 12x6 + 15x7
3x²(4x³ + 5x4 + 6x5
6x5 + 8x6 + 10x7

Expand 4x(5x2 - 2xy).

9x³ - 6xy

20x³ - 8x²

20x³ - 8x²y

9x³ - 6x²y

Only two of these sets of brackets have been expanded correctly.

Tick those two.

2gh(3g + 5g²) = 6g²h + 10g³h

2gh(g + 5g²) = 2gh + 10g³

2gh(3gh + 5g²) = 6g²h + 10g³h

2gh(3gh + 5g²) = 6g²h² + 10g³h

Expand 5a³b²(2ab² + 4a²b²).

7a4b4 + 9a5b4

7a4b4 + 9a6b4

10a3b4 + 20a6b4

10a4b4 + 20a5b4

  • Question 1

Expand 3a3(a5 - 3a)

CORRECT ANSWER
3a8 - 9a4
EDDIE SAYS
3a8 - 9a4 is the correct answer. 3a³ × a5 = 3a8 3a³ × × -3a = - 9a4
  • Question 2

Match the expressions with brackets to the correct expanded versions.

CORRECT ANSWER

Column A

Column B

x(x² + 2)
x³ + 2x
3x(x² + 2)
3x³ + 6x
3x3(x² + 2)
3x5 + 6x
3x3(5x² + 2)
15x5 + 6x3
EDDIE SAYS
Make sure you use index laws when expanding brackets. Have a look at 3x3(5x² + 2). 3x3 × 5x² = 15x5 3x3 × 2 = 6x3
  • Question 3

Expand this bracket: 2y³(2y4 - 3y)

CORRECT ANSWER
4y7 - 6y4
EDDIE SAYS
You need to use index laws to expand this bracket. 2y³ × 2y4 = 4y7 2y³ × - 3y = - 6y4 So the answer is 4y7 - 6y4.
  • Question 4

Which of these will expand to give 36x8 - 12x5?

CORRECT ANSWER
6x5(6x3 - 2)
6x5(6x3 - 2)
4x2(9x6 - 3x3)
EDDIE SAYS
The only bracket that will not expand to 36x8 - 12x5 is: 9x4(4x2 - 3x). Instead, it expands to 36x6 - 27x5.
  • Question 5

Spot the mistake!

Underline the part of the expression which has been expanded incorrectly.

7x3(3x² + 2x) = 21x6 + 14x4

CORRECT ANSWER
21x6 + 14x4
EDDIE SAYS
21x6 is incorrect. 7x3 × 3x² = 21x5 We add the powers when multiplying with indices.
  • Question 6

Expand 5x⊃(2x² + 3x4 - x³).

CORRECT ANSWER
10x4 + 15x6 - 5x5
EDDIE SAYS
Don't worry that there are three terms in the bracket here! The process is exactly the same. 5x⊃ × 2x² = 10x4 5x⊃× 3x4 = 15x6 5x⊃ × - x³ = - 5x5 The correct answer is 10x4 + 15x6 - 5x5.
  • Question 7

Match the brackets to the correct expansions.

CORRECT ANSWER

Column A

Column B

2x²(3x³ + 4x4
6x5 + 8x6 +...
3x²(3x³ + 4x4
9x5 + 12x6 ...
2x²(4x³ + 5x4
8x5 + 12x6 ...
3x²(4x³ + 5x4
12x5 + 15x6...
EDDIE SAYS
.
  • Question 8

Expand 4x(5x2 - 2xy).

CORRECT ANSWER
20x³ - 8x²y
EDDIE SAYS
4x × 5x² = 20x³ 4x × -2xy = - 8x²y Don't forget about the y! You cannot simplify it using index law, but you must not let it disappear!
  • Question 9

Only two of these sets of brackets have been expanded correctly.

Tick those two.

CORRECT ANSWER
2gh(3g + 5g²) = 6g²h + 10g³h
2gh(3gh + 5g²) = 6g²h² + 10g³h
EDDIE SAYS
Did you remember to apply the laws of indices to each of the letters? 2gh(g + 5g²) = 2gh + 10g³ is incorrect. It should be 2g²h + 10g³h. 2gh(3gh + 5g²) = 6g²h + 10g³h is also incorrect. The correct answer should be 6g²h² + 10g³h.
  • Question 10

Expand 5a³b²(2ab² + 4a²b²).

CORRECT ANSWER
10a4b4 + 20a5b4
EDDIE SAYS
10a4b4 + 20a5b4 is the correct answers. 5a³b² × 2ab² = 10a4b4 5a³b² × 4a²b² = 20a5b4
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