134r. Review Like Terms and Simplifying Expressions

Learning Intentions

• To understand that like terms contain exactly the same pronumerals, possibly in a different order
• decide if two terms are like terms
• combine like terms to Simplify expressions

Pre-requisite Summary

• Know that a term is a part of an expression separated by or signs
• Know that a coefficient is the number multiplying the pronumeral part of a term
• Understand that pronumerals stand for numbers
• Be able to Identify the pronumerals in a term
• Know that multiplication can be written without the sign, for example
• Understand that the order of pronumerals in a product does not change the term, for example

Worked Examples

Worked Example 1

State whether each pair of terms is like terms:

a) and

b) and

c) and

Worked Example 2

State whether each pair of terms is like terms:

a) and

b) and

c) and

Worked Example 3

Combine like terms to simplify:

a)

b)

c)

Worked Example 4

Combine like terms to simplify:

a)

b)

c)

Worked Example 5

Simplify each expression by combining like terms:

a)

b)

c)

Worked Example 6

Simplify each expression by combining like terms:

a)

b)

c)

Problems

Problem 1

State whether each pair of terms is like terms:

a) and

b) and

c) and

Problem 2

State whether each pair of terms is like terms:

a) and

b) and

c) and

Problem 3

Combine like terms to simplify:

a)

b)

c)

Problem 4

Combine like terms to simplify:

a)

b)

c)

Problem 5

Simplify each expression by combining like terms:

a)

b)

c)

Problem 6

Simplify each expression by combining like terms:

a)

b)

c)

Exercises

Understanding and Fluency

Exercise 1.

State whether each pair of terms is like terms:

a) and

b) and

c) and

d) and

Exercise 2.

State whether each pair of terms is like terms:

a) and

b) and

c) and

d) and

Exercise 3.

Combine like terms to simplify:

a)

b)

c)

d)

Exercise 4.

Combine like terms to simplify:

a)

b)

c)

d)

Exercise 5.

Simplify each expression:

a)

b)

c)

d)

Exercise 6.

Simplify each expression:

a)

b)

c)

d)

Exercise 7.

Decide which terms are like terms, then simplify:

a)

b)

c)

d)

Exercise 8.

Fill in the blank to make like terms:

a)

b)

c)

d)

Reasoning

Exercise 9.

Explain why and are like terms.

Exercise 10.

A student says that and are like terms because both contain . Explain the mistake.

Exercise 11.

Noah says that and are like terms because both contain . Is he correct? Explain.

Exercise 12.

Explain why only like terms can be combined when simplifying an expression.

Exercise 13.

A student simplifies to . Describe the error.

Problem-solving

Exercise 14.

A shop sells pens for dollars each and notebooks for dollars each. A customer buys pens, notebooks and then more pens. Write and simplify the total cost.

Exercise 15.

A rectangle has side lengths and . Write an expression for the sum of the two lengths and simplify it.

Exercise 16.

A student scores points in round one, points in round two, and then more points in round three. Write and simplify the total score.

Exercise 17.

A bag contains red counters, blue counters and another red counters. Write and simplify the total number of counters in terms of and .

Exercise 18.

A builder uses tiles in one section, tiles in another section, and removes tiles. Write and simplify the final number of tiles.

Exercise 19.

A pattern has squares in one row and squares in another row. Write and simplify the total number of squares.

Potential Misunderstandings

• Students may think terms are like terms just because they share one pronumeral
• Students may think coefficients must be the same for terms to be like terms
• Students may not Recognise that and represent the same pronumeral part
• Students may think and are like terms
• Students may combine unlike terms into a single product, such as turning into
• Students may forget to include the sign of a term when combining like terms
• Students may combine constant terms with variable terms incorrectly
• Students may overlook that a term with no written coefficient has coefficient

Next: 135r. Review Multiplying and Dividing Terms