Factorise 6xy - 4y + 6 -9x by regrouping method. Please explain the regrouping of 6-9x to get the common factor 3x-2 as it is the same obtained in the 6xy -4y

Dear student,
The question should be;

      6xy - 4y + 6 - 9x= 6xy - 9x - 4y + 6=(6xy - 9x) - (4y - 6)=3x(2y - 3) - 2(2y - 3)=(2y - 3) (3x - 2)

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Factorization by regrouping is quite easy.

In the term 6-9x, take out the highest common factor which is 3 and leave the rest inside a bracket.


Similarly, in the term 6xy-4y, take out the HCF which is 2y outside and keep the rest inside a bracket.


Now,put the terms together.


Change the sign of the first term to factorise further.


Now factorise.


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