New
New
Year 9

# The product of two binomials

I can use the distributive law to find the product of two binomials.

New
New
Year 9

# The product of two binomials

I can use the distributive law to find the product of two binomials.

## Lesson details

### Key learning points

1. The distributive law can be used to find the product of two binomials.
2. An area model can be used to explore the underlying structure.
3. Both of the terms in one bracket must be multiplied by both terms in the second.

### Common misconception

Missing out partial products

Relating back to numerical examples and showing that 12 × 34 is not just 10 × 30 + 2 × 4. Using algebra tiles and area models can help to support student's understanding.

### Keywords

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

It will be really valuable for pupils to see the connection between using an area model to multiply two two-digit numbers and multiplying a binomial. Show the two side by side as much as possible.
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).

## Starter quiz

### 6 Questions

Q1.
$$2x$$ and $$5x$$ can be called __________ terms.
equivalent
identical
inverse
reciprocal
Q2.
What expression could these algebra tiles represent?
Correct answer: $$x^2 + 6x + 9$$
$$6x^2 + 9$$
$$7x + 9$$
$$4x^2 + 9x$$
$$x^2 + 15x$$
Q3.
Which is the correct area model to show the expansion of $$x(x + 3)$$?
Correct Answer: An image in a quiz
Q4.
Expand $$x(x + 8)$$.
$$2x + 8$$
$$10x$$
$$9x^2$$
$$x^2 + 8$$
Correct answer: $$x^2 + 8x$$
Q5.
Expand $$x(x - 3)$$.
$$x^2 + 3x$$
Correct answer: $$x^2 - 3x$$
$$3 - x^2$$
$$2x^2 - 3x$$
$$x^2 - 3$$
Q6.
Which of these calculations are the same as $$11 \times 14$$ ?
$$(10 \times 10) + (1\times 4)$$
$$(11\times 7) + (11\times 2)$$
Correct answer: $$(1 \times 14) + (10 \times 14)$$
Correct answer: $$(4\times 11) + (10\times 11)$$
$$(4\times 11) + (1\times 14)$$

## Exit quiz

### 6 Questions

Q1.
Which of these expressions are binomials?
Correct answer: $$x + 4$$
$$x^2 + 2x + 2$$
$$2x + 3x$$
Correct answer: $$x - 6$$
$$xy$$
Q2.
Here is an area model for $$(x + 2)(x + 4).$$ Which of these expressions is the correct expanded form?
$$x^2 + 2x + 8$$
$$x^2 + 4x + 4$$
Correct answer: $$x^2 + 6x + 8$$
$$x^2 + 8x + 6$$
$$3x^2 + 4x + 8$$
Q3.
Here is an area model for $$(x - 3)(x - 1).$$ Which of these is the correct expanded form?
$$x^2 -2x + 3$$
Correct answer: $$x^2 -4x + 3$$
$$x^2 -4x - 3$$
$$x^2 + 4x + 3$$
$$x^2 + 4x - 3$$
Q4.
Which product of two binomials could be represented by this area model?
$$(x - 15)( x - 8)$$
$$(x - 15)( x + 8)$$
$$(x - 10)( x + 12)$$
$$(x + 12)( x - 10)$$
Correct answer: $$(x + 15)( x - 8)$$
Q5.
Which is the correct expanded form of $$(x - 3)^2$$ ?
$$x^2 - 9$$
$$x^2 + 9$$
$$x ^2 - 6x - 9$$
Correct answer: $$x^2 - 6x + 9$$
$$x ^2 + 6x - 9$$
Q6.
Match each product of two binomials to its correct expansion.
Correct Answer:$$(x + 7)(x + 3)$$,$$x^2 + 10x + 21$$

$$x^2 + 10x + 21$$

Correct Answer:$$(x + 7)(x - 3)$$,$$x^2 + 4x - 21$$

$$x^2 + 4x - 21$$

Correct Answer:$$(x - 7)(x + 3)$$,$$x^2 - 4x - 21$$

$$x^2 - 4x - 21$$

Correct Answer:$$(x - 7)(x - 3)$$,$$x^2 - 10x + 21$$

$$x^2 - 10x + 21$$

Correct Answer:$$(x + 7)^2$$,$$x^2 + 14x + 49$$

$$x^2 + 14x + 49$$

Correct Answer:$$(x - 7)^2$$,$$x^2 - 14x + 49$$

$$x^2 - 14x + 49$$