Skip to content
Oak National Academy
Oak National Academy
Teachers
Pupils
icon-background-square
New
New
Year 9

Difference of two squares

I can use the special case when the product of two binomials is the difference of two squares.

Download all resources
arrow-right
Share activities with pupils
arrow-right
icon-background-square
New
New
Year 9

Difference of two squares

I can use the special case when the product of two binomials is the difference of two squares.

Download all resources
arrow-right
Share activities with pupils
arrow-right
warning

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.
View new resources
arrow-right

Lesson details

Key learning points

  1. The product of two binomials often produces three terms.
  2. There are cases where the coefficient of the linear term is zero.
  3. The terms in the two binomials can indicate this.
  4. You can use an area model to explore the structure.

Keywords

  • Partial product - A partial product refers to any of the multiplication results that lead up to an overall multiplication result.

  • Binomial - A binomial is an algebraic expression representing the sum or difference of exactly two unlike terms.

Common misconception

Squaring a binomial is the same as just squaring each term. This can then cause confusion with difference of two squares where expanding a pair of binomials does result in just two terms.

Using an area model and taking time to check the partial products each time, particularly with negative terms, should help students to check if they have expanded correctly.

A nice prompt for exploration might be to get students to explore the difference of numerical squares, e.g. 5^2 - 4^2 and how this is equal to 5 + 4, explore other consecutive squares and look for patterns. Explore how this relates to the algebraic difference of two squares.
speech-bubble
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

Skip lesson video

Loading...

Starter quiz

Download starter quiz

6 Questions

Q1.
A zero pair is __________.
a pair of values which sum to one
Correct answer: a pair of values which sum to zero
a pair of values which multiply to one
a pair of values which multiply to zero
a pair of values with a difference of zero
Q2.
Use this area model to help you find the correct expansion of $$(x + 3)(x + 9)$$.
An image in a quiz
$$x ^2 + 6x + 27$$
$$x^2 + 9x + 3x$$
$$x^2 + 9x + 27$$
$$x^2 + 12x + 12$$
Correct answer: $$x^2 + 12x + 27$$
Q3.
Use this area model to help you find the correct expansion of $$(x - 5)(x - 11)$$.
An image in a quiz
$$x^2 - 16x - 55$$
Correct answer: $$x^2 - 16x + 55$$
$$x^2 - 6x - 55$$
$$x^2 - 6x + 55$$
$$x^2 + 16x - 55$$
Q4.
Fill in the missing value in this simplified expansion: $$(x +8)(x - 3)\equiv x^2 +$$ $$x - 24$$.
Correct Answer: 5, +5
Q5.
Which is the correct expanded form of $$(x - 6)^2$$ ?
$$x^2 - 36$$
$$x^2 + 36$$
Correct answer: $$x^2 - 12x + 36$$
$$x^2 - 12x - 36$$
$$x^2 + 12x - 36$$
Q6.
Match each product of two binomials to its correct expansion.
Correct Answer:$$(x+3)(x+2)$$,$$x^2 + 5x + 6$$

$$x^2 + 5x + 6$$

Correct Answer:$$(x+3)(x-2)$$,$$x^2 + x - 6$$

$$x^2 + x - 6$$

Correct Answer:$$(x+2)(x-3)$$,$$x^2 - x - 6$$

$$x^2 - x - 6$$

Correct Answer:$$(x-2)(x-3)$$,$$x^2 - 5x + 6$$

$$x^2 - 5x + 6$$

Correct Answer:$$(x - 6)(x + 1)$$,$$x^2 - 5x - 6$$

$$x^2 - 5x - 6$$

Correct Answer:$$(x + 6)(x -1)$$,$$x^2 + 5x - 6$$

$$x^2 + 5x - 6$$

Exit quiz

Download exit quiz

6 Questions

Q1.
Match each product of two binomials to its simplified form.
Correct Answer:$$(x + 8)(x + 8)$$,$$x^2 + 16x + 64$$

$$x^2 + 16x + 64$$

Correct Answer:$$(x + 8)(x - 8)$$,$$x^2 - 64$$

$$x^2 - 64$$

Correct Answer:$$(x - 8)(x - 8)$$,$$x^2 - 16x + 64$$

$$x^2 - 16x + 64$$

Q2.
Which of these expressions can be written as the difference of two squares?
Correct answer: $$(x + 5)(x - 5)$$
$$(x + 6)(x - 7)$$
$$(x - 8)(x - 8)$$
Correct answer: $$(x - 9)(x + 9)$$
$$(x -11)^2$$
Q3.
Match each product of two binomials with its simplified form.
Correct Answer:$$(x + 2)(x - 2)$$,$$x^2 - 4$$

$$x^2 - 4$$

Correct Answer:$$(2 + x)(2 - x)$$,$$4 - x^2$$

$$4 - x^2$$

Correct Answer:$$(x + 4)(x - 4)$$,$$x^2 - 16$$

$$x^2 - 16$$

Correct Answer:$$(4 - x)(4 + x)$$,$$16 - x^2$$

$$16 - x^2$$

Correct Answer:$$(x - 8)(x + 8)$$,$$x^2 - 64$$

$$x^2 - 64$$

Correct Answer:$$(8 - x)(8 + x)$$,$$64 - x^2$$

$$64 - x^2$$

Q4.
Which of these show an expression written in the 'difference of two squares' form?
$$x^2 + 4$$
Correct answer: $$x^2 - 9$$
$$16 + x^2$$
$$x^2 - 2x + 1$$
Correct answer: $$y^2 - x^2$$
Q5.
Which of these expressions can be written as the difference of two squares?
$$(2a + 4)(a + 2)$$
Correct answer: $$(3a + 5)(3a - 5)$$
$$(a + y)(b - y)$$
$$(5a - 1)^2$$
Correct answer: $$(2y - 4)(2y + 4)$$
Q6.
Expand $$(3y - 4)(3y + 4)$$.
$$6y^2 - 4$$
$$6y^2 + 4$$
$$9y^2 - 8$$
Correct answer: $$9y^2 - 16$$
$$9y^2 + 16$$