Math - Reiny, Tuesday, July 26, 2011 at 10:35am
If you know the quick expansion of
(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^2, then your expression is
= (3x)^3 + 3(3x)^2(5) + 3(3x)(5)^2 + 5^3 - 3x^3 + 3x
= 27x^3 + 135x^2 + 225x + 125 - 3x^3 + 3x
= 24x^3 + 135x^2 + 228x + 125
(here is a quick way to see if your answer is correct.
pick any simple value for x
original value = (8^3) - 3(0) = 512
answer value = 24 + 135 + 228 + 125 = 512
original = 5^3 + 0 = 125
new one = 0+0+0+125 = 125
Even though this does not absolutely prove that our answer is right, the probability that I am right is very very high.
It would definitely prove my answer would be wrong if the two results would not be the same.)