This document discusses factorizing expressions. It provides examples of factorizing terms with variables like 8a - 4a = 4(2a - 1) and expressions with squared terms like 15x + 9^2 = 3(5x + 3^2). It concludes with practice problems factorizing additional expressions like 10x + 5 = 5(2x + 1) and their factorized forms.

1. October 4, 2012
Brackets and factors
2. Factorising
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2. Explanation October 4, 2012
A group of numbers and letters, such as 4b, 2y or 3x²
is known as a term.
An expression is made up from two or more terms.
4b + 9 A single number, or letter is still a term.
When you factorise, you find numbers and letters that
will multiply to make a term.
Factorising is the opposite of expanding. You end up
with an expression involving brackets.
There are a number of simple steps that you need to
follow, to factorise an expression.
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3. Example October 4, 2012
Factorising 8a – 4a
If there are two terms, draw one set ( )
of brackets.
Find the biggest number that will
multiply to make the number in both 4
terms. Write it outside the brackets.
If there is a letter in each term, write a
this outside the brackets as well.
Work out what you need to multiply
the new term you have written outside
the bracket, to produce each of the 2 –1
original terms. include the operation
symbol, “+”, or “–”.
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4. Example October 4, 2012
If you have a squared number, treat it as you would a
number that isn’t squared.
Factorise 15x + 9 ²
The common highest factor is 3 3( )
Divide the first term by 3 3(5x )
Divide the second term by 3, but 3(5x + 3² )
keep the number squared.
Notice that 9² = 81 and 3 × 3 ² = 81
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5. Practise October 4, 2012
Factorise the following…
10x + 5 5 (2x + 1)
12x – 8 4(3x – 2)
16x + 8² 8(2x + 8)
9a + 3 3(a + 1)
16x – 12x 4x(4 – 3)
12q ² – 18q 6q (2q – 3)
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End