036. Like Terms and Simplifying Expressions

Learning Intentions

• To know what like terms are
• Identify like terms within an expression
• Simplify expressions by combining like terms

Pre-requisite Summary

• Understand that a term is a part of an expression separated by addition or subtraction
• Know that a coefficient is the numerical part of a term such as the in
• Understand that a variable is a letter representing a number
• Recognise that a constant term has no variable, such as
• Be able to identify the variable part of a term, such as in
• Know that addition and subtraction Determine whether terms are separate
• Understand that only terms with the same variable part can be combined
• Be able to Substitute simple values into expressions if needed to Check reasoning

Worked Examples

Worked Example 1

a) Explain what like terms are.

b) State which terms are like in the expression .

c) State which terms are not like.

Worked Example 2

Identify the like terms in each expression:

a)

b)

c)

Worked Example 3

Simplify by combining like terms:

a)

b)

c)

Worked Example 4

Simplify by combining like terms:

a)

b)

c)

Worked Example 5

Simplify each expression:

a)

b)

c)

Worked Example 6

For each expression:

a) identify the like terms

b) combine the like terms

c) write the simplified expression

For

Problems

Problem 1

a) Explain what like terms are.

b) State which terms are like in the expression .

c) State which terms are not like.

Problem 2

Identify the like terms in each expression:

a)

b)

c)

Problem 3

Simplify by combining like terms:

a)

b)

c)

Problem 4

Simplify by combining like terms:

a)

b)

c)

Problem 5

Simplify each expression:

a)

b)

c)

Problem 6

For each expression:

a) identify the like terms

b) combine the like terms

c) write the simplified expression

For

Exercises

Understanding and Fluency

Exercise 1.

State which pairs are like terms:

a) and

b) and

c) and

Exercise 2.

State which pairs are like terms:

a) and

b) and

c) and

Exercise 3.

Identify all like terms in each expression:

a)

b)

c)

Exercise 4.

Identify all like terms in each expression:

a)

b)

c)

Exercise 5.

Simplify by combining like terms:

a)

b)

c)

Exercise 6.

Simplify by combining like terms:

a)

b)

c)

Exercise 7.

Simplify each expression:

a)

b)

c)

Exercise 8.

Simplify each expression:

a)

b)

c)

Exercise 9.

Simplify each expression:

a)

b)

c)

Exercise 10.

Simplify each expression:

a)

b)

c)

Reasoning

Exercise 11.

Explain why and are like terms but and are not like terms.

Exercise 12.

A student says . Explain the mistake.

Exercise 13.

Explain why constant terms can be combined with other constant terms.

Exercise 14.

A student simplifies to . Explain why this is incorrect.

Problem-solving

Exercise 15.

A student collects expression cards labelled , , , , and . Combine the like terms to make a simplified expression.

Exercise 16.

A shop has a cost expression of , where is the number of notebooks. Simplify the expression for the total cost.

Exercise 17.

A taxi fare is modelled by , where is the number of kilometres. Simplify the expression.

Exercise 18.

A pattern has total tiles given by , where is the step number. Simplify the expression and state the coefficient of .

Potential Misunderstandings

• Students may think terms are like terms just because they have the same coefficient
• Students may think -terms and -terms can be combined because both contain letters
• Students may combine unlike terms, for example writing
• Students may forget that constant terms are like terms with each other
• Students may split a term incorrectly, treating as two separate terms
• Students may ignore the sign in front of a term when combining like terms
• Students may think and are like terms even though their variable parts are different
• Students may combine some like terms correctly but leave others uncombined in the same expression

Next: 037. Multiplication and Division in Algebraic Expressions