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GCSE
AQA

# Algebraic expressions

Letters can be used to stand for unknown values or values that can change. Formulas can be written and equations solved in a range of problems in science and engineering.

Part of
Maths
Algebra

# Expanding brackets

To expand a bracket means to multiply each term in the bracket by the expression outside the bracket. For example, in the expression , multiply both and 7 by 3, so:

.

Expanding brackets involves using the skills of simplifying algebra. Remember that and .

Expand .

Question

Expand .

Question

Expand .

## Expanding brackets with powers

Powers or indices show how many times a number has been multiplied by itself. For example, and .

Using index laws, terms that contain powers can be simplified. Remember to use index laws when multiplying expressions that contain powers. For example:

.

### Example

Expand the bracket .

Multiply by first. and , so .

Then multiply by . and , so .

So, .

Question

Expand the bracket .

Multiply by . .

Multiply by . .

Multiply by . .

## Expanding and simplifying

Expressions with brackets can often be mixed in with other terms. For example, . In these cases first expand the bracket and then collect any like terms.

### Example 1

Expand and simplify .

### Example 2

Expand and simplify .

BIDMAS or BODMAS is the order of operations: Brackets, Indices or Powers, Divide or Multiply, Add or Subtract.

Following BIDMAS, multiplying out the bracket must happen before completing the addition, so multiply out the bracket first.

This gives:

Collecting the like terms gives .

Answers are usually written with descending order of powers.

## More Guides

1. Algebraic expressions – AQA
2. Algebraic formulae – AQA
3. Solving linear equations – AQA
4. Solving simultaneous equations – AQA
5. Solving quadratic equations – AQA
6. Inequalities – AQA
7. Sequences – AQA
8. Straight line graphs – AQA
9. Other graphs – AQA
10. Transformation of curves – Higher- AQA
11. Algebraic fractions – AQA
12. Using and interpreting graphs – AQA

Our team of exam survivors will get you started and keep you going.

Meet them here

• Skillswise: Maths
• Bitesize KS3: Maths

• Pearson Education

• Revision Buddies SUBSCRIPTION

• Revisio SUBSCRIPTION

• Seneca Learning

• Just Maths

## GCSE Subjects

1. Architecture
2. Art and Design
3. Biology (Single Science)
5. Chemistry (Single Science)
6. Combined Science
7. Computer Science
8. Design and Technology
9. Digital Technology (CCEA)
10. Drama
11. Electronics
12. Engineering
13. English Language
14. English Literature
15. Food Technology
16. French
17. Geography
18. German
19. Graphics
20. History
21. Home Economics: Food and Nutrition (CCEA)
22. ICT
23. Irish – Learners (CCEA)
24. Journalism (CCEA)
25. Learning for Life and Work (CCEA)
26. Mandarin
27. Maths
28. Maths Numeracy (WJEC)
29. Media Studies
30. Modern Foreign Languages
31. Moving Image Arts (CCEA)
32. Music
33. Physical Education
34. Physics (Single Science)
35. Product Design
36. PSHE and Citizenship
37. Religious Studies
38. Resistant Materials
39. Science
40. Sociology
41. Spanish
42. Systems and Control
43. Textiles
44. Welsh Second Language (WJEC)

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GCSE
AQA

# Algebraic expressions

Letters can be used to stand for unknown values or values that can change. Formulas can be written and equations solved in a range of problems in science and engineering.

Part of
Maths
Algebra

# Expanding brackets

To expand a bracket means to multiply each term in the bracket by the expression outside the bracket. For example, in the expression , multiply both and 7 by 3, so:

.

Expanding brackets involves using the skills of simplifying algebra. Remember that and .

Expand .

Question

Expand .

Question

Expand .

## Expanding brackets with powers

Powers or indices show how many times a number has been multiplied by itself. For example, and .

Using index laws, terms that contain powers can be simplified. Remember to use index laws when multiplying expressions that contain powers. For example:

.

### Example

Expand the bracket .

Multiply by first. and , so .

Then multiply by . and , so .

So, .

Question

Expand the bracket .

Multiply by . .

Multiply by . .

Multiply by . .

## Expanding and simplifying

Expressions with brackets can often be mixed in with other terms. For example, . In these cases first expand the bracket and then collect any like terms.

### Example 1

Expand and simplify .

### Example 2

Expand and simplify .

BIDMAS or BODMAS is the order of operations: Brackets, Indices or Powers, Divide or Multiply, Add or Subtract.

Following BIDMAS, multiplying out the bracket must happen before completing the addition, so multiply out the bracket first.

This gives:

Collecting the like terms gives .

Answers are usually written with descending order of powers.

## More Guides

1. Algebraic expressions – AQA
2. Algebraic formulae – AQA
3. Solving linear equations – AQA
4. Solving simultaneous equations – AQA
5. Solving quadratic equations – AQA
6. Inequalities – AQA
7. Sequences – AQA
8. Straight line graphs – AQA
9. Other graphs – AQA
10. Transformation of curves – Higher- AQA
11. Algebraic fractions – AQA
12. Using and interpreting graphs – AQA

Our team of exam survivors will get you started and keep you going.

Meet them here

• Skillswise: Maths
• Bitesize KS3: Maths

• Pearson Education

• Revision Buddies SUBSCRIPTION

• Revisio SUBSCRIPTION

• Seneca Learning

• Just Maths

## GCSE Subjects

1. Architecture
2. Art and Design
3. Biology (Single Science)
5. Chemistry (Single Science)
6. Combined Science
7. Computer Science
8. Design and Technology
9. Digital Technology (CCEA)
10. Drama
11. Electronics
12. Engineering
13. English Language
14. English Literature
15. Food Technology
16. French
17. Geography
18. German
19. Graphics
20. History
21. Home Economics: Food and Nutrition (CCEA)
22. ICT
23. Irish – Learners (CCEA)
24. Journalism (CCEA)
25. Learning for Life and Work (CCEA)
26. Mandarin
27. Maths
28. Maths Numeracy (WJEC)
29. Media Studies
30. Modern Foreign Languages
31. Moving Image Arts (CCEA)
32. Music
33. Physical Education
34. Physics (Single Science)
35. Product Design
36. PSHE and Citizenship
37. Religious Studies
38. Resistant Materials
39. Science
40. Sociology
41. Spanish
42. Systems and Control
43. Textiles
44. Welsh Second Language (WJEC)

## Explore the BBC

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Homepage

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BBC iD

Search

GCSE
AQA

# Algebraic expressions

Letters can be used to stand for unknown values or values that can change. Formulas can be written and equations solved in a range of problems in science and engineering.

Part of
Maths
Algebra

# Expanding brackets

To expand a bracket means to multiply each term in the bracket by the expression outside the bracket. For example, in the expression , multiply both and 7 by 3, so:

.

Expanding brackets involves using the skills of simplifying algebra. Remember that and .

Expand .

Question

Expand .

Question

Expand .

## Expanding brackets with powers

Powers or indices show how many times a number has been multiplied by itself. For example, and .

Using index laws, terms that contain powers can be simplified. Remember to use index laws when multiplying expressions that contain powers. For example:

.

### Example

Expand the bracket .

Multiply by first. and , so .

Then multiply by . and , so .

So, .

Question

Expand the bracket .

Multiply by . .

Multiply by . .

Multiply by . .

## Expanding and simplifying

Expressions with brackets can often be mixed in with other terms. For example, . In these cases first expand the bracket and then collect any like terms.

### Example 1

Expand and simplify .

### Example 2

Expand and simplify .

BIDMAS or BODMAS is the order of operations: Brackets, Indices or Powers, Divide or Multiply, Add or Subtract.

Following BIDMAS, multiplying out the bracket must happen before completing the addition, so multiply out the bracket first.

This gives:

Collecting the like terms gives .

Answers are usually written with descending order of powers.

## More Guides

1. Algebraic expressions – AQA
2. Algebraic formulae – AQA
3. Solving linear equations – AQA
4. Solving simultaneous equations – AQA
5. Solving quadratic equations – AQA
6. Inequalities – AQA
7. Sequences – AQA
8. Straight line graphs – AQA
9. Other graphs – AQA
10. Transformation of curves – Higher- AQA
11. Algebraic fractions – AQA
12. Using and interpreting graphs – AQA

Our team of exam survivors will get you started and keep you going.

Meet them here

• Skillswise: Maths
• Bitesize KS3: Maths

• Pearson Education

• Revision Buddies SUBSCRIPTION

• Revisio SUBSCRIPTION

• Seneca Learning

• Just Maths

## GCSE Subjects

1. Architecture
2. Art and Design
3. Biology (Single Science)
5. Chemistry (Single Science)
6. Combined Science
7. Computer Science
8. Design and Technology
9. Digital Technology (CCEA)
10. Drama
11. Electronics
12. Engineering
13. English Language
14. English Literature
15. Food Technology
16. French
17. Geography
18. German
19. Graphics
20. History
21. Home Economics: Food and Nutrition (CCEA)
22. ICT
23. Irish – Learners (CCEA)
24. Journalism (CCEA)
25. Learning for Life and Work (CCEA)
26. Mandarin
27. Maths
28. Maths Numeracy (WJEC)
29. Media Studies
30. Modern Foreign Languages
31. Moving Image Arts (CCEA)
32. Music
33. Physical Education
34. Physics (Single Science)
35. Product Design
36. PSHE and Citizenship
37. Religious Studies
38. Resistant Materials
39. Science
40. Sociology
41. Spanish
42. Systems and Control
43. Textiles
44. Welsh Second Language (WJEC)

## Explore the BBC

• Home
• News
• Sport
• Weather
• iPlayer
• Sounds
• CBBC
• CBeebies
• Food
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• Make It Digital
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• Local
• Tomorrow's World
• TV

Homepage

• Accessibility Help
BBC iD

Search

GCSE
AQA

# Algebraic expressions

Letters can be used to stand for unknown values or values that can change. Formulas can be written and equations solved in a range of problems in science and engineering.

Part of
Maths
Algebra

# Expanding brackets

To expand a bracket means to multiply each term in the bracket by the expression outside the bracket. For example, in the expression , multiply both and 7 by 3, so:

.

Expanding brackets involves using the skills of simplifying algebra. Remember that and .

Expand .

Question

Expand .

Question

Expand .

## Expanding brackets with powers

Powers or indices show how many times a number has been multiplied by itself. For example, and .

Using index laws, terms that contain powers can be simplified. Remember to use index laws when multiplying expressions that contain powers. For example:

.

### Example

Expand the bracket .

Multiply by first. and , so .

Then multiply by . and , so .

So, .

Question

Expand the bracket .

Multiply by . .

Multiply by . .

Multiply by . .

## Expanding and simplifying

Expressions with brackets can often be mixed in with other terms. For example, . In these cases first expand the bracket and then collect any like terms.

### Example 1

Expand and simplify .

### Example 2

Expand and simplify .

BIDMAS or BODMAS is the order of operations: Brackets, Indices or Powers, Divide or Multiply, Add or Subtract.

Following BIDMAS, multiplying out the bracket must happen before completing the addition, so multiply out the bracket first.

This gives:

Collecting the like terms gives .

Answers are usually written with descending order of powers.

## More Guides

1. Algebraic expressions – AQA
2. Algebraic formulae – AQA
3. Solving linear equations – AQA
4. Solving simultaneous equations – AQA
5. Solving quadratic equations – AQA
6. Inequalities – AQA
7. Sequences – AQA
8. Straight line graphs – AQA
9. Other graphs – AQA
10. Transformation of curves – Higher- AQA
11. Algebraic fractions – AQA
12. Using and interpreting graphs – AQA

Our team of exam survivors will get you started and keep you going.

Meet them here

• Skillswise: Maths
• Bitesize KS3: Maths

• Pearson Education

• Revision Buddies SUBSCRIPTION

• Revisio SUBSCRIPTION

• Seneca Learning

• Just Maths

## GCSE Subjects

1. Architecture
2. Art and Design
3. Biology (Single Science)
5. Chemistry (Single Science)
6. Combined Science
7. Computer Science
8. Design and Technology
9. Digital Technology (CCEA)
10. Drama
11. Electronics
12. Engineering
13. English Language
14. English Literature
15. Food Technology
16. French
17. Geography
18. German
19. Graphics
20. History
21. Home Economics: Food and Nutrition (CCEA)
22. ICT
23. Irish – Learners (CCEA)
24. Journalism (CCEA)
25. Learning for Life and Work (CCEA)
26. Mandarin
27. Maths
28. Maths Numeracy (WJEC)
29. Media Studies
30. Modern Foreign Languages
31. Moving Image Arts (CCEA)
32. Music
33. Physical Education
34. Physics (Single Science)
35. Product Design
36. PSHE and Citizenship
37. Religious Studies
38. Resistant Materials
39. Science
40. Sociology
41. Spanish
42. Systems and Control
43. Textiles
44. Welsh Second Language (WJEC)

## Explore the BBC

• Home
• News
• Sport
• Weather
• iPlayer
• Sounds
• CBBC
• CBeebies
• Food
• Bitesize
• Earth
• Arts
• Make It Digital
• Taster
• Local
• Tomorrow's World
• TV