Discussion
If x + y = k, then 3x2 + 6xy + 3y2 =
| (A) | k |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
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
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
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