1. A1 Introduction to algebra
S1–S4 Mathematics
A1 Introduction to algebra

2. Contents
Factorizing Expressions

3. Factorizing expressions
Factorizing an expression is the opposite of expanding it.
Expanding or multiplying out
Factorizing
a(b + c)
ab + ac
Often:
When we expand an expression we remove the brackets.
When we factorize an expression we write it with brackets.

4. Factorizing expressions
Expressions can be factorized by dividing each term by a common factor and writing this outside a pair of brackets.
For example, in the expression
5x + 10
the terms 5x and 10 have a common factor, 5.
We can write the 5 outside of a set of brackets and mentally divide 5x + 10 by 5.
We can write the 5 outside of a set of brackets
Encourage pupils to check this by multiplying the expression out to 5x + 10.
(5x + 10) ÷ 5 = x + 2
This is written inside the bracket.
5(x + 2)
5(x + 2)

5. Factorizing expressions
Writing 5x + 10 as 5(x + 2) is called factorizing the expression.
Factorize 6a + 8
Factorize 12 – 9n
The highest common factor of 6a and 8 is
The highest common factor of 12 and 9n is 2. 3.
(6a + 8) ÷ 2 =
3a + 4
(12 – 9n) ÷ 3 =
4 – 3n
For each example start by asking pupils to give you the highest number or term that will divide into both terms in the expression.
6a + 8 =
2(3a + 4)
12 – 9n =
3(4 – 3n)

6. Factorizing expressions
Writing 5x + 10 as 5(x + 2) is called factorizing the expression.
Factorize 3x + x2
Factorize 2p + 6p2 – 4p3
The highest common factor of 3x and x2 is
The highest common factor of 2p, 6p2 and 4p3 is x.
2p.
(2p + 6p2 – 4p3) ÷ 2p =
(3x + x2) ÷ x =
3 + x
Again, for each example ask pupils to give you the highest number or term that will divide into every term in the given expression.
1 + 3p – 2p2
3x + x2 =
x(3 + x)
2p + 6p2 – 4p3 =
2p(1 + 3p – 2p2)

7. Factorization
Start by asking pupils to give you the value of the highest common factor of the two terms. Reveal this and then ask pupils to give you the values of the terms inside the brackets.
The activities at the end of A1.3 Multiplying terms and expanding brackets can also be used to practice factorization.