Factor the polynomial completely 27-y^3

Question

anonymous · Answer

There is a pretty simple formula for the difference of square which is $$a^3 + b^3 = (a - b)(a^2 +ab + b^2)$$ so a = y and b = 27. Try it from there

anonymous · Answer

would y =1?

anonymous · Answer

no y is just a general variable factoring isn't trying to find the values of y. Since this is just an EXPRESSION not an EQUATION y could be any number because there are no restrictions

anonymous · Answer

so it would be (y-27)(y^2+27y+27^2)?? then would i FOIL?

anonymous · Answer

nope this is the factorization of the original expression

anonymous · Answer

so what would i do after this step?

anonymous · Answer

27-y^(3)

The binomial can be factored using the difference of cubes formula, because both terms are perfect cubes.  The difference of cubes formula is a^(3)-b^(3)=(a-b)(a^(2)+ab+b^(2)).
(3-y)(9+3y+y^(2))