## Discussion

If *x* + *y* = *k,* then 3*x*^{2} + 6*xy* + 3*y*^{2} =

(A) | |

(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 ?

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!

I understand everything up to the point of factoring out 3.. Im puzzled about what to do next?

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

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?

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