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FACTORISATION


Factorisation is the opposite process of expanding brackets. For example, expanding brackets would require 2(x+1) to be written as 2x+2. Factorisation would be to start with 2x+2 and to end up with 2(x +1).
Factorisation-128x89
The two expressions 2(x+1) and 2x+2 are equivalent; they have the same value for all values of x. COMMON FACTORS

Factorising based on common factors relies on there being factors common to all the terms. For example, 2x-6×2 can be factorised as follows:

2x-6×2=2x(1-3x)
Factorisation using a switch around in brackets
Question
Factorise: 5(a-2)-b(2-a).


Answer

Use a ‘switch around’ strategy to find the common factor.

Notice that 2-a=-(a-2) 5(a-2)-b(2-a)=5(a-2)-[-b(a-2)] =5(a-2)+b(a-2) =(a-2)(5+b)
Difference of two squares
We have seen that (ax+b)(ax-b) can be expanded to a 2×2-b2 Therefore a2x2-b2 can be factorised as (ax+b)(ax-b)
For example, x2-16 can be written as x2-42 which is a difference of two squares. Therefore, the factors of x2-16 are (x-4) and (x+4). To spot a difference of two squares, look for expressions:

1). consisting of two terms;

2). with terms that have different signs (one positive, one negative);

3). with each term a perfect square.

For example: a2-1; 4×2-y2; -49+p4.
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