## Accessibility links

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# Bitesize

# 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.

# 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 .

### Example

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 .

## More Guides

- Algebraic expressions – AQA
- Algebraic formulae – AQA
- Solving linear equations – AQA
- Solving simultaneous equations – AQA
- Solving quadratic equations – AQA
- Inequalities – AQA
- Sequences – AQA
- Straight line graphs – AQA
- Other graphs – AQA
- Transformation of curves – Higher- AQA
- Algebraic fractions – AQA
- Using and interpreting graphs – AQA

## Struggling to get your head round revision and exams?

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

Meet them here

## Links

Sign in, choose your GCSE subjects and see content that's tailored for you.

- Skillswise: Maths
- Radio 4: Maths collection
- Bitesize KS3: Maths

Pearson Education

Revision Buddies SUBSCRIPTION

Revisio SUBSCRIPTION

Seneca Learning

Just Maths

## Accessibility links

- Skip to content
- Accessibility Help

Notifications

# Bitesize

# 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.

# 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 .

### Example

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 .

## More Guides

- Algebraic expressions – AQA
- Algebraic formulae – AQA
- Solving linear equations – AQA
- Solving simultaneous equations – AQA
- Solving quadratic equations – AQA
- Inequalities – AQA
- Sequences – AQA
- Straight line graphs – AQA
- Other graphs – AQA
- Transformation of curves – Higher- AQA
- Algebraic fractions – AQA
- Using and interpreting graphs – AQA

## Struggling to get your head round revision and exams?

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

Meet them here

## Links

Sign in, choose your GCSE subjects and see content that's tailored for you.

- Skillswise: Maths
- Radio 4: Maths collection
- Bitesize KS3: Maths

Pearson Education

Revision Buddies SUBSCRIPTION

Revisio SUBSCRIPTION

Seneca Learning

Just Maths

## Accessibility links

- Skip to content
- Accessibility Help

Notifications

# Bitesize

# 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.

# 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 .

### Example

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 .

## More Guides

- Algebraic expressions – AQA
- Algebraic formulae – AQA
- Solving linear equations – AQA
- Solving simultaneous equations – AQA
- Solving quadratic equations – AQA
- Inequalities – AQA
- Sequences – AQA
- Straight line graphs – AQA
- Other graphs – AQA
- Transformation of curves – Higher- AQA
- Algebraic fractions – AQA
- Using and interpreting graphs – AQA

## Struggling to get your head round revision and exams?

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

Meet them here

## Links

Sign in, choose your GCSE subjects and see content that's tailored for you.

- Skillswise: Maths
- Radio 4: Maths collection
- Bitesize KS3: Maths

Pearson Education

Revision Buddies SUBSCRIPTION

Revisio SUBSCRIPTION

Seneca Learning

Just Maths

## Accessibility links

- Skip to content
- Accessibility Help

Notifications

# Bitesize

# Algebraic expressions

# Expanding brackets

.

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

### Example

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 .

.

### 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

### Example 1

Expand and simplify .

### Example 2

Expand and simplify .

This gives:

Collecting the like terms gives .

## More Guides

- Algebraic expressions – AQA
- Algebraic formulae – AQA
- Solving linear equations – AQA
- Solving simultaneous equations – AQA
- Solving quadratic equations – AQA
- Inequalities – AQA
- Sequences – AQA
- Straight line graphs – AQA
- Other graphs – AQA
- Transformation of curves – Higher- AQA
- Algebraic fractions – AQA
- Using and interpreting graphs – AQA

## Struggling to get your head round revision and exams?

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

Meet them here

## Links

Sign in, choose your GCSE subjects and see content that's tailored for you.

- Skillswise: Maths
- Radio 4: Maths collection
- Bitesize KS3: Maths

Pearson Education

Revision Buddies SUBSCRIPTION

Revisio SUBSCRIPTION

Seneca Learning

Just Maths