Table of contents 
FACTORISATION USING COMMON FACTORS 
FACTORISATION BY REGROUPING TERMS 
Solved Examples: 
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• Factorisation means to write an expression as a product of its factors.
• Prime factor, an irreducible factor, a factor which cannot be expressed further as a product of factors.
• Some expressions can easily be factorised using these identities:
I. a^{2} + 2ab + b^{2} = (a + b)^{2}
II. a^{2} – 2ab + b^{2} = (a – b)^{2}
III. a^{2} – b^{2} = (a – b)(a + b)
IV. x^{2} + (a + b)x + ab = (x + a)( x+ b)
• The number 1 is a factor of every algebraic term, but it is shown only when needed.
• When factorisation of x^{2} + (a + b)x + ab is done by splitting the middle term, the two numbers which give the product ab and (a + b) as the coefficient of x have to be chosen very carefully with correct sign.
We Know That
(i) (a + b)^{2} = a^{2} + b^{2} + 2ab
(ii) (a – b)^{2} = a^{2} + b^{2} – 2ab
(iii) a^{2} – b^{2} = (a + b)(a – b)
(iv) 1 is a factor of every term of an algebraic expression. Unless it is specially required, we do not show 1 as a separate factor of any term.
(v) Factorisation means writing an expression as product of factors.
Example 1: Write 10y as irreducible factor form.Note:
In case of factorisation of a term of an expression, the word ‘irreducible’ is used in place of ‘prime’. For example, 6pq = 2 * 3 * pq is not the irreducible form because pq can further be factorised as p q, i.e. the irreducible form of 6pq = 2 * 3 * p * q.
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