Discussion
If x
+ y = k, then 3x 2 + 6xy + 3y2 =
*This question is included in Nova Press: Problem Solving Diagnostic Test, question #14
| (A) | k |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 05/16/2012 21:59
When i get to the part of perfect square trinomial i get lost and dont understand how to continue the problem to get the answer 3k^2
Posted: 05/17/2012 00:48
Liz, it's simply reducing the polynomial into its perfect square form. See the attached for how (x+y)^2 is expanded into the polynomial. The solution step you were referring to is simply doing the reverse. You should memorize this algebraic identity.
Posted: 12/28/2012 21:44
Arcadia. You are a genius. So simple and yet so complex. Thanks
Posted: 05/17/2012 12:08
Okay i see now thank You for the help!
Posted: 07/28/2016 11:18
Can you walk me through this problem? I'm not quite grasping it
Posted: 07/28/2016 15:40
Hi Chelsea,
In the method shown above, we manipulated the expression 3x^2 + 6xy + 3y^2 to dig out the expression x + y and then replaced x + y with k. Let's do this again and show a few more steps:
3x^2 + 6xy + 3y^2 =
3(x^2 + 2xy + y^2 ) = by factoring out the common factor 3
3(x + y)^2 = by the perfect square trinomial formula x^2 + 2xy + y^2 = (x + y)^2
Notice that we have now dug out the expression x + y, and we are give that x + y equals k. So, replacing x + y in the expression 3(x + y)^2 with k yields
3(k)^2 =
3k^2 by dropping the unnecessary parentheses.
Nova Press
In the method shown above, we manipulated the expression 3x^2 + 6xy + 3y^2 to dig out the expression x + y and then replaced x + y with k. Let's do this again and show a few more steps:
3x^2 + 6xy + 3y^2 =
3(x^2 + 2xy + y^2 ) = by factoring out the common factor 3
3(x + y)^2 = by the perfect square trinomial formula x^2 + 2xy + y^2 = (x + y)^2
Notice that we have now dug out the expression x + y, and we are give that x + y equals k. So, replacing x + y in the expression 3(x + y)^2 with k yields
3(k)^2 =
3k^2 by dropping the unnecessary parentheses.
Nova Press