SOLUTION: Can you please assist me with the following: 27x^3+y^3, I understand how to get to (3x)^3+y^3 and to factor out 3x+y, the solution shows (3x+y)[(3x)^2-(3x)(y)+y^2] as the next ste

Question 398212: Can you please assist me with the following:
27x^3+y^3, I understand how to get to (3x)^3+y^3 and to factor out 3x+y, the solution shows (3x+y)[(3x)^2-(3x)(y)+y^2] as the next step, I understand the first and last expression but do not understand the middle -(3x)(y) Can you please explain how I can recognize this?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
27x^3+y^3, I understand how to get to (3x)^3+y^3 and to factor out 3x+y, the solution shows (3x+y)[(3x)^2-(3x)(y)+y^2] as the next step, I understand the first and last expression but do not understand the middle -(3x)(y) Can you please explain how I can recognize this?
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Familiarize yourself with the following forms:
Difference of cubes: a^3-b^3 = (a-b)(a^2+ab+b^2)
----
Sum of cubes: a^3+b^3 = (a+b)(a^2-ab+b^2)
===========================================
You have (3x)^3+y^3
so you factor and get (3x+y)((3x)^2-(3x)y)+y^2)
= (3x+y)(9x^2-3xy+y^2)
============================
Cheers,
Stan H.
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