Question 77225
If we have something like this:

{{{ax^2+bx+c}}}

If we look at the last term, we can determine if the trinomial is a perfect square. If the last term is a perfect square, then we take the square root and then double that value to get the middle term. If the middle term equals {{{2*sqrt(c)}}} and c is a perfect square, then we have a trinomial that is a perfect square. Since 48 is not a perfect square, the entire trinomial is not a perfect square. It's that simple. This idea can be applied to something like this:


{{{x^2+6x+9}}}

Since 9 is a perfect square, we take the square root of 9 to get 3, and then double 3 to get 6. This shows that the trinomial {{{x^2+6x+9}}} is a perfect square.