## Discussion

If x + y = k, then 3x2 + 6xy + 3y2 =

 (A) k (B) ... (C) ... (D) ... (E) ... (F) ...
*This question is included in Nova Math - Diagnostic/Review:, question #14

The solution is

Posted: 03/08/2012 19:30
I do not understand where the (x+y)^2 came from ?
Posted: 03/09/2012 01:33
Crystal, it comes from first factoring out 3, which gives us 3(x^2 + 2xy + y^2). We recognize that the resulting term in the bracket is a square of (x+y)^2. This is something you should remember from algebra. Since x+y = k, ...
Posted: 02/03/2013 11:20
What happened to the 2xy in the equation?
Posted: 02/03/2013 11:21
Never mind. I figured it out. Thanks!
Posted: 04/07/2013 15:24
I understand everything up to the point of factoring out 3.. Im puzzled about what to do next?
Posted: 04/07/2013 17:48
Hi Ivana,

Using the Perfect Square Trinomial formula, we rewrote

x^2 + 2xy + y^2

as

(x + y)^2

So 3(x^2 + 2xy + y^2) became 3(x + y)^2.

Since we are given that x + y = k, 3(x + y)^2 became 3k^2.

Nova Press
Posted: 07/26/2019 06:38
I don’t understand why x^2 + 2xy + y^2 = (x+y)^2. I would understand if it were just x^2 +y^2 but how did we get rid of 2xy?
Posted: 07/26/2019 13:48
Hi Chan,

There is no theory behind it. x^2 + 2xy + y^2 is just what results when we multiply out the expression (x+y)^2 by the foil method:

(x+y)^2 =

(x+y)(x+y) =

x^2 + xy + xy + y^2 =

Now, adding the like terms xy + xy gives

x^2 + 2xy + y^2 You need to be signed in to perform that action.