Skip to content
Skip to content
Teachers
Go to pupils
View unit
New
New
Lesson 4 of 13
  • Year 10
  • Foundation

Checking and securing understanding of expanding a single bracket

I can use the distributive law to multiply an expression by a term.

View unit
Lesson 4 of 13
New
New
  • Year 10
  • Foundation

Checking and securing understanding of expanding a single bracket

I can use the distributive law to multiply an expression by a term.

Lesson details

Key learning points

  1. The term could have any form such as fractional or algebraic and may contain exponents.
  2. The expression may be comprised of multiple terms.
  3. If either the term or expression are identical to another term or expression, these can be combined.

Keywords

  • Distributive law - The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.

Common misconception

Pupils find simplifying expressions which are the difference of two bracketed expressions difficult.

There are two equivalent methods detailed in learning cycle two. Spend time on both, getting pupils to explore their equivalence. If pupils are struggling, considering subtraction as adding the negative value is the easiest to model.


To help you plan your year 10 maths lesson on: Checking and securing understanding of expanding a single bracket, download all teaching resources for free and adapt to suit your pupils' needs...

Explore the use of algebra tiles when expanding a single bracket to help when pupils find the product of two binomials in the future. Using these representations can be a really useful tool for all abilities and are used to demonstrate structures such as completing the square later.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), 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...

Prior knowledge starter quiz

Download quiz pdf

6 Questions

Q1.
Evaluate the expression $$\frac{3x}{2x + 5}$$ for $$x = 3$$. Write your answer as a decimal.

Correct Answer: 0.82

Q2.
Evaluate the expression $$\frac{x}{x + 1}$$ for $$x = 4$$. Write your answer as a decimal.

Correct Answer: 0.8

Q3.
A company buys pencils in bulk for £2 per pen and sells them for £3.25 each. If the company sells $$x$$ pens, which of the following shows the correct expression for the profit, 'p'?

Correct answer: $$p = 1.25x$$
$$p = 3x$$
$$p = 3x + 2$$

Q4.
If a taxi charges a £15 base fare plus £2 per mile, which of the following represents the total cost, $$c$$, for a trip of $$x$$ miles?

$$c = 15x$$
$$c = 15x + 2$$
Correct answer: $$c = 2x + 15$$

Q5.
A savings account offers 5% annual interest compounded yearly. If $$x$$ pounds are deposited, which expression represents the amount, $$a$$, in the account after one year?

$$a = 2x + 0.05x$$
Correct answer: $$a = 1.05x$$
$$a = x(1 + 0.05)^2$$

Q6.
A book store sells a book for £20, which is 20% more than its cost price. What is the cost price, 'p', of the book?

$$p = 20 - 0.2 \times 30$$
Correct answer: $$p = \frac{20}{1.2}$$
$$p = 20 + 0.2 \times 30$$

Assessment exit quiz

Download quiz pdf

6 Questions

Q1.
Expand $$5(x + 7) + 3(4x + 5)$$ and simplify where possible.

$$20x + 40$$
Correct answer: $$17x + 50$$
$$23x + 35$$
$$17x + 35$$

Q2.
Expand $$2(3x - 4) - 5(x - 6)$$ and simplify where possible.

Correct answer: $$x + 22$$
$$-x + 22$$
$$6x - 8$$
$$x - 30$$

Q3.
Expand $$-4(x - 5) + 2(2x + 3)$$ and simplify where possible.

$$-x - 2$$
$$-4x + 14$$
Correct answer: $$26$$
$$-4x - 14$$

Q4.
Expand $$3(x^2 - 2x) + 4(x - 3)$$ and simplify where possible.

Correct answer: $$3x^2 - 2x - 12$$
$$3x^2 - 6x - 12$$
$$3x^2 + 2x - 12$$
$$3x^2 + x - 12$$

Q5.
Expand $$-2(x^2 + 3x) - 3(2x - 4)$$ and simplify where possible.

Correct answer: $$-2x^2 - 12x + 12$$
$$-2x^2 - 6x + 12$$
$$-2x^2 - 6x - 12$$
$$-2x^2 + 3x - 12$$

Q6.
Expand $$4(2x - 3)^2 - 5(3x + 2)$$ and simplify where possible.

$$16x^2 - 24x + 9 - 15x - 10$$
$$16x^2 - 24x - 6$$
$$16x^2 - 63x - 26$$
Correct answer: $$16x^2 - 63x + 26$$