I presumed I was right in taking 3(a^2 + b^2) - a(b + 2a) +2b(a+3b) down to 3a^2 + 3b^2 - ab + 2a^2 + 2ba + 6b
my friend just said he thinks im going about it in the wrong way??
(ab = ba, so it's best to write all mixed terms in the same order)
Now you need to collect like terms (otherwise you have just expanded the brackets not simplified them):
3(a^2 + b^2) - a(b + 2a) +2b(a+3b) = (3a^3-2a^2) +(-ab+ 2ab) + (3b^2+6b^2) = a^2 + ab + 9b^2