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SAI International School
                                                    CLASS – VIII,
           SUB: MATHEMATICS

           LESSON NOTES-3
           Ch14: FACTORISATION

           SUBTOPIC:
               Factorisation by regrouping terms
               What is regrouping?


              1) Factorisation by regrouping terms:-

                  In some algebraic expressions, it is not possible that every term has a common factor.
                  Look at the expression 2xy + 2y + 3x + 3. You will notice that the first two terms have
                  common factors 2 and y and the last two terms have a common factor 3. But there is
                  no single factor common to all the terms.
                  Let us write (2xy + 2y) in the factor form:
                                    2xy + 2y = (2 × x × y) + (2 × y)                 (Do the factorisation)
                                              = (2 × y × x) + (2 × y × 1)      ( 1 is multiplicative identity)
                                              = (2y × x) + (2y × 1)           (Write the HCF as one term)
                                              = 2y (x + 1)            (Distributive property of multiplication)


                  Similarly,         3x + 3 = (3 × x) + (3 × 1)                    (Do the factorisation)
                                              = 3 × (x + 1)           (Distributive property of multiplication)
                                               = 3 ( x + 1)
                  Hence, 2xy + 2y + 3x + 3 = 2y (x + 1) + 3 (x +1)
                  Observe, now we have a common factor (x + 1) in both the terms on the right hand
                  side. Combining the two terms,
                          2xy + 2y + 3x + 3 = 2y (x + 1) + 3 (x + 1)
                                             = (x + 1) (2y + 3) (Ans)
                              The expression 2xy + 2y + 3x + 3 is now in the form of a product of factors.
                  It’s factors are (x + 1) and (2y + 3). Note, these factors are irreducible.
                        Try to do the factorisation of the above problem by other way and find a new
                         irreducible algebraic term , and compare it with the given answer?


              2) What is regrouping?


                  Suppose, the above expression was given as 2xy + 3 + 2y + 3x; then it will not be easy
                  to see the factorisation. Rearranging the expression, as 2xy + 2y + 3x + 3, allows us to
                  form groups (2xy + 2y) and (3x + 3) leading to factorisation. This is regrouping.
                        In the regrouping method we use a group of algebraic term to factorise the given
                         term.
                        We have to see that is the common group will appear after taking the common.
                        If necessary then change the place of the terms in the question to get a better
                         group to take common.
                        If the terms are written with assign + or – then we can change their place with
                         the given sign
                        In this method we can factorise more than two algebraic terms
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