I know that is first,outer, inner, last but are there other ways to solve using the method?
If you have a expression , then you could re-write it as , and calculate from there.
So for example:
Essentially, it's the same as foil method. Essential, all ways of expanding the expression are very close to foil method. Can't really go wrong :P.
For example: to multiply (a+ b)(c+ d) I can use "FOIL": "First" terms, ab; "Outside terms", ad; "Inside" terms, bc; "Last" terms, bd. Adding all of those: ab+ ad+ bc+ bd.
I could have got the same result by using the rule: Multiply the first term in the first expression, a, by each of the terms in the second expression: a(c+ c)= ac+ ad. Then multiply the second term in the first expression by each of the terms in the second expression: b(c+ d)= bc+ bd. Adding those: ac+ ad+ bc+ bd, exactly as above.
If I have 3 terms in, say, the first expression, like (a+ b+ c)(u+ v), I can't use "FOIL" exactly but I can think:
Multiply the first term in the first expression, a, by every term in the second expression- a(u+ v)= au+ av.
Multiply the second term in the first expression, b, by every term in the second expression- b(u+ v)= bu+ bv.
Multiply the third term in the first expression, c, by every term in the second expression- c(u+ v)= cu+ cv.
Now add all of those: (a+ b+ c)(u+ v)= au+ av+ bu+ bv+ cu+ cv.