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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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Year 10

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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Lesson details

Key learning points

An expression can be described as being factorised.
An expression is fully factorised if the highest common factor has been taken out.
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.

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.

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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.
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: $$p = (2.25-1.2)x$$

$$p = 2.25x - 1.2$$

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 $$2(x - 3) + 4(2x + 1)$$ and simplify where possible.

Correct Answer: 10x - 2

Q5.
Simplify $$3(x + 2)^2 - (x - 1)(x + 1)$$ where possible.

Correct answer: $$2x^2 + 12x + 13$$

$$3x^2 + 12x + 7$$

$$4x^2 + 12x + 7$$

Q6.
Factorise $$4x^2 - 16$$ completely.

$$(2x + 4)(2x - 4)$$

$$(2x)^2 - 4^2$$

Correct answer: $$4(x-2)(x+2)$$

Assessment exit quiz

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6 Questions

Q1.
Fully factorise the expression $$5x + 20$$

Correct answer: $$5(x + 4)$$

$$x(5 + 20)$$

$$25(x + 4)$$

$$5(x - 4)$$

Q2.
Fully factorise the expression $$3y^2 + 12y$$

$$3y(y^2 + 4)$$

$$15y(y + 4)$$

$$3(y^2 + 4)$$

Correct answer: $$3y(y + 4)$$

Q3.
Fully factorise the expression $$4z - 8z^2$$

$$-4z(z - 1)$$

Correct answer: $$4z(1 - 2z)$$

$$12z(1 - 2z)$$

$$-8z(z - 2)$$

Q4.
Fully factorise the expression $$6m^2 + 24m + 18$$

$$2(3m^2 + 12m + 9)$$

Correct answer: $$6(m^2 + 4m + 3)$$

$$6(m + 2)^2$$

$$6(m + 3)(m + 1)$$

Q5.
Fully factorise the expression $$8x^2 - 20x + 12$$.

$$8(x^2 - 2.5x + 1.5)$$

$$2(4x^2 - 10x + 6)$$

Correct answer: $$4(2x^2 - 5x + 3)$$

$$2(2x - 3)(2x - 2)$$

Q6.
Fully factorise the expression $$7y^2 - 14y$$.

Correct answer: $$7y(y - 2)$$

$$7(y^2 - 2)$$

$$14y(y - 1)$$

$$7(y - 2)(y + 2)$$

Lesson appears in

UnitMaths / Algebraic manipulation

Maths

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Checking and securing understanding of factorising

Checking and securing understanding of factorising

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

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?

Q2.What is the value of $$x$$ in $$2x + 3 = 15$$

Q3.Simplify $$3ax + 9ax + 13ax + b$$

Q4.Expand $$2(x - 3) + 4(2x + 1)$$ and simplify where possible.

Q5.Simplify $$3(x + 2)^2 - (x - 1)(x + 1)$$ where possible.

Q6.Factorise $$4x^2 - 16$$ completely.

Assessment exit quiz

6 Questions

Q1.Fully factorise the expression $$5x + 20$$

Q2.Fully factorise the expression $$3y^2 + 12y$$

Q3.Fully factorise the expression $$4z - 8z^2$$

Q4.Fully factorise the expression $$6m^2 + 24m + 18$$

Q5.Fully factorise the expression $$8x^2 - 20x + 12$$.

Q6.Fully factorise the expression $$7y^2 - 14y$$.

Lesson appears in

UnitMaths / Algebraic manipulation

Maths

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?

Q2.
What is the value of $$x$$ in $$2x + 3 = 15$$

Q3.
Simplify $$3ax + 9ax + 13ax + b$$

Q4.
Expand $$2(x - 3) + 4(2x + 1)$$ and simplify where possible.

Q5.
Simplify $$3(x + 2)^2 - (x - 1)(x + 1)$$ where possible.

Q6.
Factorise $$4x^2 - 16$$ completely.

Q1.
Fully factorise the expression $$5x + 20$$

Q2.
Fully factorise the expression $$3y^2 + 12y$$

Q3.
Fully factorise the expression $$4z - 8z^2$$

Q4.
Fully factorise the expression $$6m^2 + 24m + 18$$

Q5.
Fully factorise the expression $$8x^2 - 20x + 12$$.

Q6.
Fully factorise the expression $$7y^2 - 14y$$.