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

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.

=3(2-3x).

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

=2y(3x-2)

Now,put the terms together.

3(2-3x)+2y(3x-2)

Change the sign of the first term to factorise further.

=-3(-2+3x)+2y(3x-2)

Now factorise.

(3x-2)(2y-3)