New
New
Year 10
Higher

Checking and securing understanding of factorising

I can use the distributive law to factorise expressions where there is a common factor.

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New
New
Year 10
Higher

Checking and securing understanding of factorising

I can use the distributive law to factorise expressions where there is a common factor.

Link copied to clipboard

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Lesson details

Key learning points

  1. An expression can be described as being factorised.
  2. An expression is fully factorised if the highest common factor has been taken out.
  3. The distributive law can help us factorise an expression.

Keywords

  • Factor - A factor is a term which exactly divides another term.

  • Factorise - To factorise is to express a term as the product of its factors.

Common misconception

Leaving answers which are not fully factorised when they are required to.

There should be a focus on reading questions to decipher what they are being asked to do. When they have to fully factorise they need the highest common factor of all the terms. LC3 focuses on situations where they are not going to fully factorise.


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

Use algebra tiles to consolidate the idea that factorising is finding expressions that multiply to give the required expression. When factorising with algebra tiles, pupils should be building rectangles. This can be revisited when factorising quadratics.
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

6 Questions

Q1.
A bakery sells x cakes for £2.25 each. If the cost to make each cake is £1.20, what is the profit, p, for selling all the cakes?
p=1.2x
Correct answer: p=(2.251.2)x
p=2.25x1.2
Q2.
What is the value of x in 2x+3=15
Correct Answer: 6
Q3.
Simplify 3ax+9ax+13ax+b
Correct Answer: 25ax + b, b + 25ax
Q4.
Expand 2(x3)+4(2x+1) and simplify where possible.
Correct Answer: 10x - 2
Q5.
Simplify 3(x+2)2(x1)(x+1) where possible.
Correct answer: 2x2+12x+13
3x2+12x+7
4x2+12x+7
Q6.
Factorise 4x216 completely.
(2x+4)(2x4)
(2x)242
Correct answer: 4(x2)(x+2)

6 Questions

Q1.
Fully factorise the expression 5x+20
Correct answer: 5(x+4)
x(5+20)
25(x+4)
5(x4)
Q2.
Fully factorise the expression 3y2+12y
3y(y2+4)
15y(y+4)
3(y2+4)
Correct answer: 3y(y+4)
Q3.
Fully factorise the expression 4z8z2
4z(z1)
Correct answer: 4z(12z)
12z(12z)
8z(z2)
Q4.
Fully factorise the expression 6m2+24m+18
2(3m2+12m+9)
Correct answer: 6(m2+4m+3)
6(m+2)2
6(m+3)(m+1)
Q5.
Fully factorise the expression 8x220x+12.
8(x22.5x+1.5)
2(4x210x+6)
Correct answer: 4(2x25x+3)
2(2x3)(2x2)
Q6.
Fully factorise the expression 7y214y.
Correct answer: 7y(y2)
7(y22)
14y(y1)
7(y2)(y+2)
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