#a + 2c + 3b = 0# then what is # a ^3 + 8 b ^3 + 27c^3#?

1 Answer
Feb 18, 2015

We can rewrite one of the letters as an expression in the others.

#a+2c+3b=0->a=-2c-3b#

Then we replace every #a# in the second expression:

#a^3+8b^3+27c^3=#
#(-2c-3b)^3+8b^3+27c^3=#
#(-8c^3-36bc^2-54b^2c-19b^3)+8b^3+27c^3=#

#19c^3-36bc^2-54b^2c-10b^3#

Extra :
If the first expression had been #a+2b+3c=0#
(and I suspect that it was!!)

Then the #b^3#'s and #c^3#'s would have cancelled out nicer.

#a=-2b-3c#
#(-2b-3c)^3+8b^3+27c^3=#
#(-8b^3-36b^2c-54bc^2-27c^3)+8b^3+27c^3=#

#-36b^2c-54bc^2 or 18bc(-2b-3c)#
and, since #a=-2b-3c# we can rewrite that:

Answer:
#a^3+8b^3+27c^3=18abc#