038e. Expanding Brackets

Learning Intentions

• To understand what it means to Expand brackets
• expand brackets Use repeated terms or rectangle areas
• expand brackets using the distributive law

Pre-requisite Summary

• Understand that multiplication can be written in different ways, such as , , or
• Know that a bracket can represent a grouped quantity
• Understand addition of like terms such as
• Be able to Simplify simple algebraic expressions
• Understand that the area of a rectangle is found by multiplying length by width
• Recognise that the distributive law connects multiplication with addition and subtraction

Worked Examples

Worked Example 1

a) Explain what it means to expand .

b) Write as repeated terms.

c) Simplify the expanded expression.

Worked Example 2

Use repeated terms or a rectangle model to expand:

a)

b)

Worked Example 3

Use a rectangle area model to expand:

a)

b)

Worked Example 4

Use the distributive law to expand:

a)

b)

c)

Worked Example 5

Use the distributive law to expand:

a)

b)

c)

Worked Example 6

Expand and simplify:

a)

b)

c)

Problems

Problem 1

a) Explain what it means to expand .

b) Write as repeated terms.

c) Simplify the expanded expression.

Problem 2

Use repeated terms or a rectangle model to expand:

a)

b)

Problem 3

Use a rectangle area model to expand:

a)

b)

Problem 4

Use the distributive law to expand:

a)

b)

c)

Problem 5

Use the distributive law to expand:

a)

b)

c)

Problem 6

Expand and simplify:

a)

b)

c)

Exercises

Understanding and Fluency

Exercise 1.

Expand using repeated terms:

a)

b)

c)

Exercise 2.

Expand using repeated terms or a rectangle model:

a)

b)

c)

Exercise 3.

Expand using the distributive law:

a)

b)

c)

Exercise 4.

Expand using the distributive law:

a)

b)

c)

Exercise 5.

Expand:

a)

b)

c)

Exercise 6.

Expand:

a)

b)

c)

Exercise 7.

Expand and simplify:

a)

b)

c)

Exercise 8.

Expand and simplify:

a)

b)

c)

Reasoning

Exercise 9.

Explain why means .

Exercise 10.

A student says . Explain the mistake.

Exercise 11.

Explain how a rectangle model can show that .

Exercise 12.

A student expands as . Explain why this is incorrect.

Problem-solving

Exercise 13.

A rectangle has width and length . Write and expand an expression for its area.

Exercise 14.

A rectangle has width and length . Write and expand an expression for its area.

Exercise 15.

A student buys bags, and each bag contains marbles. Write and expand an expression for the total number of marbles.

Exercise 16.

A machine makes parts each hour. Expand the expression for the number of parts made in one hour.

Exercise 17.

A garden has rows, each with plants. Write and expand an expression for the total number of plants.

Exercise 18.

A builder lays tiles in two equal sections. Expand the expression for the total number of tiles.

Potential Misunderstandings

• Students may think expanding brackets means removing the brackets without changing the expression correctly
• Students may multiply only the first term inside the bracket and forget the others
• Students may confuse addition inside brackets with multiplication outside brackets
• Students may not recognise that means three groups of
• Students may misuse the rectangle area model by not multiplying each part of the length by the width
• Students may Apply the distributive law to addition incorrectly, for example writing
• Students may make sign errors when expanding brackets with subtraction
• Students may expand correctly but not simplify the final expression

Next: 039. Algebraic Modelling with Expressions