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Year 7

Factorising expressions

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

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New
New
Year 7

Factorising expressions

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

Download all resources
Share activities with pupils

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.

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.

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.

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 (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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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: $$2d^2e$$
$$2de$$
$$2d^2$$

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: $$-3ab^2d(2ab+13a^2b^2c)$$
$$3ab^2d(-2ab-13a^2b^3c)$$