SOLUTION: Factorise: 27b^3-a^3-3a^2-3a-1

Question 1094589: Factorise:
27b^3-a^3-3a^2-3a-1
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Factorise:
27b^3-a^3-3a^2-3a-1
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Notice that (a^3 + 3a^2 + 3a + 1) = (a+1)^3
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So it's a difference of 2 cubes.
a^3 - b^3 = (a-b)*(a^2 + ab + b^2)

Answer by greenestamps(13202) (Show Source): You can put this solution on YOUR website!

This is an ugly, unusual one....

A clue to finding a way to factor it is that only the first term contains b. So separate that term from the others and see what the expression looks like:

(27b^3) + (-a^3-3a^2-3a-1)
or
(27b^3) - (a^3+3a^2+3a+1)

Do you see what to do with it from there?

(hint: what kind of factoring rules do you know that involve a term like 27b^3?)
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