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

Answer 1

Eli Assouline

One of the letters can be rewritten to represent an idea 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#

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Answer 2

Eva Abramson

(a^3 + 8b^3 + 27c^3) is equal to zero.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.