Arcadia. You are a genius. So simple and yet so complex. Thanks

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