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.

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.

## 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.

### 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.

### 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.

### 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).

## 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 $$(x + 3)(x + 9)$$.
$$x ^2 + 6x + 27$$
$$x^2 + 9x + 3x$$
$$x^2 + 9x + 27$$
$$x^2 + 12x + 12$$
Correct answer: $$x^2 + 12x + 27$$
Q3.
Use this area model to help you find the correct expansion of $$(x - 5)(x - 11)$$.
$$x^2 - 16x - 55$$
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: $$(x +8)(x - 3)\equiv x^2 +$$ $$x - 24$$.
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

### 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: $$9y^2 - 16$$
$$9y^2 + 16$$