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Checking and securing understanding of expanding a single bracket

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

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Lesson 4 of 13

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Year 10

Checking and securing understanding of expanding a single bracket

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

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Lesson details

Key learning points

The term could have any form such as fractional or algebraic and may contain exponents.
The expression may be comprised of multiple terms.
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.

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.

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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).

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Prior knowledge starter quiz

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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

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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: $$16x^2 - 63x + 26$$

Lesson appears in

UnitMaths / Algebraic manipulation

Maths

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Checking and securing understanding of expanding a single bracket

Checking and securing understanding of expanding a single bracket

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

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

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

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'?

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?

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?

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?

Assessment exit quiz

6 Questions

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

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

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

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

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

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

Lesson appears in

UnitMaths / Algebraic manipulation

Maths

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

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

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'?

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?

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?

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?

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

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

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

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

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

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