Question

Factor 27y^3-125

Answer 1

(3y-5)(9y^2+15y+25)

Answer 2

Where does the (3y)^3-(5)^3 come from?

Answer 3

You have a difference of cubes:
27y^3 - 125 = (3y)^3 - 5^3

A difference of cubes factors this way:

\[a ^{3} - b ^{3} = (a - b)(a ^{2} + ab + b ^{2})\]

Answer 4

In your case, a = 3y and b = 5, so you have
27y^3 - 125 = (3y)^3 - 5^3 =
(3y - 5)[(3y)^2 + (3y)(5) + 5^2] =
(3y - 5)(9y^2 + 15y + 25)

Answer 5

Thank you :)