Question 924361: I'm doing a problem online and it says that:
a * a^3 + 3a^2b + 3ab^2 + b^3 = a^4 + 3a^3b + 3a^2b^2 + ab^3 + 0b^4. I have no idea where the 0b^4 is coming from. Can anyone explain this? Thanks!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! it has to be a computer glitch.
there's no mathematical reason for it to be there.
the only reason i can think for it to be there would be that (a+b)^4 ends in b^4 when you are dealing with the binomial expansion theorem.
in fact, your original equation is the binomial expansion of (a+b)^3.
that leads me to believe that this is something like an aberrated application of (a+b)^4 where the computer doesn't know to remove 0b^4.
consider:
(a+b) * a = a^2 + ab
now consider:
(a+b) * (a + 0b)
you could get 0b * b = 0b^2 at the end.
in the middle it handles it ok but in the end it sticks out because the algorithm didn't know how to finish the job completely.
(a+b) * (a + 0b) is equal to a*a + a*0b + b*a + 0b*b
this can be simplified to:
a^2 + 0*a*b + a*b + 0*b*b
simplify this further and you get:
a^2 + a*b + 0*b^2
the computer was able to handle 0*a*b + a*b which resulted in a*b.
the computer didn't think it had to do anything else with 0*b*b so it left it as 0*b^2.
bottom line is it doesn't really belong there.
i'm not sure what you were supposed to do with that problem, but i would guess if you got the answer wrong because of that situation, then you have an argument to change that decision.
it's not technically wrong because 0*b^4 is equal to 0, but it doesn't really belong there.
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