# Is ( x + 3 ) 2 </msup> a trinomial or binomial since it can be expanded to

Is $\left(x+3{\right)}^{2}$ a trinomial or binomial since it can be expanded to ${x}^{2}+6x+9$
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Leslie Rollins
Note that, explicitly, a polynomial takes the form
${a}_{0}+{a}_{1}x+{a}_{2}{x}^{2}+{a}_{3}{x}^{3}+\cdots +{a}_{n}{x}^{n}$
Thus, the expression $\left(x+3{\right)}^{2}$ does not fit into this form until you expand it out into ${x}^{2}+6x+9$. Thus, since it fits the form above for a polynomial, and has three terms, we would indeed call it a trinomial.
The best you could get otherwise is that $\left(x+3{\right)}^{2}$ is the square of a binomial.