081e. Expanding Brackets and Simplifying Expressions

Learning Intentions

• Expand brackets and collect like terms in algebraic expressions
• To understand that expanding brackets and collecting like terms is a useful technique when solving equations involving brackets

Pre-requisite Summary

• Know that a term is a part of an expression separated by or signs
• Know that like terms have the same pronumeral part, such as and
• Know how to Use the distributive property, for example
• Know that when solving equations, the goal is to keep both sides equal
• Know basic one-step and two-step equation solving Use inverse operations

Worked Examples

Worked Example 1

Expand and Simplify:

Worked Example 2

Expand and simplify:

Worked Example 3

Expand and simplify:

Worked Example 4

Solve:

Worked Example 5

Solve:

Worked Example 6

Solve:

Problems

Problem 1

Expand and simplify:

Problem 2

Expand and simplify:

Problem 3

Expand and simplify:

Problem 4

Solve:

Problem 5

Solve:

Problem 6

Solve:

Exercises

Understanding and Fluency

Exercise 1.

Expand and simplify.

a)

b)

c)

Exercise 2.

Expand and simplify.

a)

b)

c)

Exercise 3.

Expand and simplify.

a)

b)

c)

Exercise 4.

Expand and simplify.

a)

b)

c)

Exercise 5.

Solve.

a)

b)

c)

Exercise 6.

Solve.

a)

b)

c)

Exercise 7.

Solve.

a)

b)

c)

Exercise 8.

Expand and simplify.

a)

b)

c)

Reasoning

Exercise 9.

Noah says . Explain why Noah is incorrect.

Exercise 10.

Without fully solving, decide which equation would be easier to solve first by expanding brackets, and explain why.

a)

b)

Exercise 11.

Mia simplified as . Identify the error and write the correct expansion.

Exercise 12.

Explain why collecting like terms cannot combine and .

Problem-solving

Exercise 13.

A rectangle has width cm and length cm. Write and simplify an expression for its perimeter.

Exercise 14.

Tickets to a school concert cost $6 each, and there is a $4 booking fee. Write and simplify an expression for the total cost of buying tickets.

Exercise 15.

A gardener plants rows of flowers, with flowers in each row, then adds more flowers. Write an expression and simplify it.

Exercise 16.

The equation represents a number puzzle. Solve the value of .

Potential Misunderstandings

• A student may multiply the number outside the bracket by only the first term and forget the second term
• A student may not treat a negative sign outside the bracket as multiplying every term inside
• A student may combine unlike terms, such as adding and to make
• A student may collect like terms before expanding brackets, even when the terms are not yet like terms
• A student may expand brackets correctly in an equation but then forget to keep both sides balanced
• A student may think expanding brackets changes the value of an expression, rather than rewriting it in an equivalent form
• A student may solve an equation involving brackets but not Check the solution in the original equation

Next: 082. Using Formulas by Substitution and Solving