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Lesson 16 of 17
  • Year 7

Factorising expressions

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

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View unit
Lesson 16 of 17
New
New
  • Year 7

Factorising expressions

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

Download all

Lesson details

Key learning points

  1. An expression can be described as being factorised.
  2. An expression can be described as being fully factorised.
  3. The distributive law can help us factorise an expression.
  4. It is important to check the expression is fully factorised.

Keywords

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

  • Fully factorise - To fully factorise is to factorise to the point that remaining term or terms cannot be factorised any further.

Common misconception

2(3y+9) is not factorised.

It is factorised; just not fully. The distinction is important as sometimes it can be beneficial to not fully factorise.


To help you plan your year 7 maths lesson on: Factorising expressions, download all teaching resources for free and adapt to suit your pupils' needs...

The use of manipulatives is really powerful here. Giving pupils physical manipulatives that they can use to 'group' expressions in various ways can aid understanding.
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

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Prior knowledge starter quiz

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6 Questions

Q1.
$$1, 2, 3, 6, z, 2z, 3z$$ and $$6z$$ are __________ of $$18yz$$ and $$24xz$$

Correct answer: common factors
products
common multipliers
variables

Q2.
List all the factors of $$7xy$$

$$7, x, y$$
$$7, 7x, 7y$$
$$7, 7x, 7y, 7xy$$
$$1, 7, 7x, 7y, 7xy$$
Correct answer: $$1, 7, x, 7x, y, 7y, xy, 7xy$$

Q3.
Which is not a factor pair for $$30ab^2c$$ ?

$$3ab \times 10bc$$
$$2ab \times 15bc$$
Correct answer: $$2abc \times 15bc$$
$$abc \times 30b$$
$$b^2 \times 30ac$$

Q4.
List the common factors of $$5cd$$ and $$35de$$

Correct answer: $$1, 5, d, 5d$$
$$1, 5$$
$$d, 5d$$
$$1, 5d$$
$$35cde, 70cde, 105cde...$$

Q5.
Find the highest common factor of the terms $$8ab$$ and $$20b^2$$

$$b$$
$$2$$
$$2b$$
Correct answer: $$4b$$
$$4$$

Q6.
Find the HCF of the terms in the expression $$6d^3e^2f -8d^2ef^2+10d^3e$$

$$6d^2e$$
$$4d^2e$$
Correct answer: $$2d^2e$$
$$2de$$
$$2d^2$$

Assessment exit quiz

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6 Questions

Q1.
To __________ is to express a term as a product of its factors.

multiply
expand
Correct answer: factorise
simplify

Q2.
Which of the below factorises the expression $$10x+20$$

Correct answer: $$2(5x+10)$$
Correct answer: $$10(x+2)$$
Correct answer: $$5(2x+4)$$
$$10(x+20)$$
$$8x+16+2x+4$$

Q3.
Match the expressions to their factorised form.

Correct Answer:$$3e+9$$,$$3(e+3)$$

$$3(e+3)$$

Correct Answer:$$9-3e$$,$$3(3-e)$$

$$3(3-e)$$

Correct Answer:$$-3e-9$$,$$-3(e+3)$$

$$-3(e+3)$$

Correct Answer:$$3e^2+9$$,$$3(e^2+3)$$

$$3(e^2+3)$$

Correct Answer:$$3e^2+9e$$,$$3e(e+3)$$

$$3e(e+3)$$

Q4.
The difference between $$2(5y+15)$$ and $$10(y+3)$$ is that the latter is factorised.

Correct Answer: fully

Q5.
Which of the below is not fully factorised?

$$6(3x-y)$$
$$3(6x-y)$$
$$6y(3x-y)$$
Correct answer: $$6y(3x-xy)$$
$$6(3x-y-3)$$

Q6.
Factorise $$-6a^2b^3d-39a^3b^4cd$$

Correct answer: $$3ab^2d(-2ab-13a^2b^2c)$$
$$3ab^2d(-2abd-13a^2b^2cd)$$
Correct answer: $$-3ab^2d(2ab+13a^2b^2c)$$
$$3ab^2d(-2ab-13a^2b^3c)$$