What is 'grouping' and how does it work?
Grouping is essentially factorisation, it's just the idea that ax + bx = (a+b)x, which we already know. But the difficulty is in recognising this relationship when x is more complicated, for example when x= 2n+3 and when a and b are also more complicated.
e.g Solve (3n^2+4n)(2n+3) + 32n+48=0
Now initially this looks awful but if you can spot that 16 goes into both 32n and 48 you can simplify it to
(3n^2+4n)(2n+3) + 16(2n+3)= 0
2n+3 is a common factor so we can rewrite this as:
(2n+3)(3n^2 +4n+16)= 0 and the question is now just a matter of solving that quadratic. This is a simple idea that crops up A LOT later on in the course, so it's really important to be able to spot that relationship.
FH
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