Match the expressions
Some of the expressions below are the same. Match up the ones that are
equal then write the others in a way similar to the others.
4(y – 2)
4y – 2y²
3(y + 4)
10 – 5y
y(y + 2)
4y – 8
2y² - 4y
2y(y – 2)
y(4 – 2y)
y² + 2y
Answers
4(y – 2)
4y – 2y²
3(y + 4)
10 – 5y
y(y + 2)
4y – 8
5(2 – y)
2y² - 4y
2y(y – 2)
y² + 2y
y(4 – 2y)
3y + 12
Factorising
Expressions
Learning outcomes
All – To be able to factorise simple expressions
with common integer factors
Most – To be able to factorise an expression into
one pair of brackets
Some – To be able to factorise quadratic
expressions
An example
To factorise an expression we write it using
brackets and take out all the common
1. Find the highest common
factors. What is the
factor of the numbers
largest factor
Examples of 12 and 16?
2. Look for any common
unknown factors
4
1.
12a - 16
3. Write the common factors
4x3xa
4x4
Common factors?
Now add any unknowns
So
outside the brackets
4. Write what is left inside the
brackets
(Rembering the operation
+/-)
12a – 16 = 4 ( 3a – 4 )
Example 2
Remember to follow each step.
What is the
largest factor
of 15 and 10?
5
Examples
2.
15ab2 + 10b
5x3xaxbxb
Common factors?
Now add any unknowns
So
5x2xb
1. Find the highest common
factor of the numbers
2. Look for any common
unknown factors
3. Write the common factors
outside the brackets
4. Write what is left inside the
brackets
(Rembering the operation
+/-)
15ab2 + 10b = 5b ( 3ab + 2 )
Questions
Factorise the following expressions
1. 3x – 9
2. 10 + 4b
3. 12c – 18c2
4. 20xy + 16x2
5. 5 – 35x
Task 2
Intermediate GCSE book
Page 228
Ex 19.6
Start with Q2
Factorising
Quadratics
Aim – For students to be able to factorise
simple quadratics where the coefficient of
x2=1
Level – GCSE grade B
Recap
Simplify the expression (x + a)(x + b)
(x + a)(x + b)
F – First
O – Outside
I – Inside
L – Last
Note – use FOIL
x × x = x2
x × b = bx
a × x = ax
a × b = ab
x2 + bx + ax + ab
= x2 + (a + b)x + ab
So …
(x + a)(x + b) = x2 + (a + b)x + ab
This is useful when factorising quadratics because…
 The coefficient of x is ‘a + b’
 The numberical part is ‘a × b’
Example –
Factorise x2 + 7x + 12
You are looking for two numbers a and b s.t.
a + b = 7 and ab = 12
1 + 6 = 7 but 1 × 6 = 6 – No good
3 + 4 = 7 and 3 × 4 = 12 – Great! Let a = 3 and b = 4
So
x2 + 7x + 12 = (x + 3)(x + 4)
More difficult!
Example
Factorise x2 – 4x – 5
You are looking for two numbers a and b s.t.
a + b = -4 and ab = -5
Note – If their product is
negative one must be
2 + -6 = -4 but 2 × -6 = -12 – No good
negative
1 + -5 = -4 and 1 × -5 = -5 – Great! Let a = 1 and b = -5
Therefore
x2 – 4x – 5 = (x + 1)(x – 5)
Task
Factorise each of the following expressions
1. x2 + 4x + 3
2. x2 + 8x + 15
3. x2 + 9x + 20
4. x2 – 3x – 4
5. x2 – 7x – 30
6. x2 + 4x – 12
7. x2 – 5x + 6
Answers
1.
2.
3.
4.
5.
6.
7.
x2 + 4x + 3 = (x + 1)(x + 3)
x2 + 8x + 15 = (x + 3)(x + 5)
x2 + 9x + 20 = (x + 4)(x + 5)
x2 – 3x – 4 = (x – 4)(x + 1)
x2 – 7x – 30 = (x – 10)(x + 3)
x2 + 4x – 12 = (x – 2)(x + 6)
x2 – 5x + 6 = (x – 2)(x – 3)