I'm trying to help my son with his homework and I have no idea where to go with this one. Here goes...
Janelle wants to enlarge a square graph that she has made so that the sides of the graph will be 1 inch more than twice the original side s. What trinomial expression represents the area of the enlarged graph?
Ok -so a trinomial is x2 + bx + c = 0
Is the answer:
x2 + 2x + 1 = 0
That is a general expression that describes quadratic equations (although incomplete, the complete one says \(\displaystyle ax^2+bx+c\)).
Trinomial is a name for any polynomial with three terms (for example \(\displaystyle a+3c+2b\), where \(\displaystyle a\), \(\displaystyle 3c\) and \(\displaystyle 2b\) are terms).
This problem requires your son to know a formula that is called a "square of a binomial". So, as Jeff implied, you have the new length of a graph and you need a trinomial expression that represents the area of enlarged graph.
Text of the problem reveals that the new, enlarged graph has the length of its side, that is one inch longer than TWICE the old size, \(\displaystyle s\). So, the new side has a length of \(\displaystyle 2s+1\).
The area of the square is the length of it's side multiplied by itself, in other words squared. So, the new area is \(\displaystyle (2s+1)^2\). In order to square this binomial, you need to use the square of a binomial formula. The result of squaring a binomial is a trinomial, so that will be your answer.
Square of a binomial:
\(\displaystyle (a+b)^2=a^2+2ab+b^2\)
\(\displaystyle (a-b)^2=a^2-2ab+b^2\)
I will leave it to you to complete the answer to this problem.
By the way, Jeff is completely right. Getting the answer without the work invested in its obtaining is counterproductive. It would be better if you introduced your son to this forum so he can seek help on his own. Getting the answer "on the plate" is not the point, investing time into getting it (even if you don't succeed on your own) is what it's all about.