1. Match the expressions 4(y – 2) 4y – 2y² 3(y + 4) 10 – 5y y(y + 2)
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)
y² + 2y
y(4 – 2y)

2. Answers 4(y – 2) 4y – 2y² 3(y + 4) 10 – 5y y(y + 2) 4y – 8 5(2 – y)

3. 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

4. What is the largest factor of 12 and 16?
An example
To factorise an expression we write it using brackets and take out all the common factors.
Examples
1. 12a - 16
Find the highest common factor of the numbers
Look for any common unknown factors
Write the common factors outside the brackets
Write what is left inside the brackets
(Rembering the operation +/-)
What is the largest factor of 12 and 16? 4
4 x 3
x a
4 x 4
Common factors?
Now add any unknowns
So 12a – 16 =
4 ( ) 3a – 4

5. What is the largest factor of 15 and 10?
Example 2
Remember to follow each step.
Examples
2. 15ab2 + 10b
Find the highest common factor of the numbers
Look for any common unknown factors
Write the common factors outside the brackets
Write what is left inside the brackets
(Rembering the operation +/-)
What is the largest factor of 15 and 10? 5
5 x 3
x a x b x b
5 x 2
x b
Common factors?
Now add any unknowns
So 15ab2 + 10b =
5b ( )
3ab 2 +

6. Questions Factorise the following expressions 3x – 9 10 + 4b
12c – 18c2
20xy + 16x2
5 – 35x

7. Task 2
Intermediate GCSE book
Page 228
Ex 19.6 Start with Q2

8. Factorising Quadratics
Aim – For students to be able to factorise simple quadratics where the coefficient of x2=1
Level – GCSE grade B

9. Simplify the expression (x + a)(x + 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

10. (x + a)(x + b) = 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)

11. Note – If their product is negative one must be negative
More difficult!
Example
Factorise x2 – 4x – 5
You are looking for two numbers a and b s.t.
a + b = -4 and ab = -5
= -4 but 2 × -6 = -12 – No good
= -4 and 1 × -5 = -5 – Great! Let a = 1 and b = -5
Therefore
x2 – 4x – 5 = (x + 1)(x – 5)
Note – If their product is negative one must be negative

12. Task Factorise each of the following expressions x2 + 4x + 3

13. Answers x2 + 4x + 3 = (x + 1)(x + 3) x2 + 8x + 15 = (x + 3)(x + 5)