We are given the expression (5/6x + 4)^2 and we are asked to express it as a trinomial in the simplest form.
To do this, we will be using the FOIL method. FOIL stands for First-Outer-Inner-Last.
The product will then be:
[tex]\begin{gathered} (\frac{5}{6}x+4)^2=(\frac{5}{6}x+4)(\frac{5}{6}x+4) \\ \\ (\frac{5}{6}x+4)^2=(\frac{5}{6}x)^2+(\frac{5}{6}x)(4)+(4)(\frac{5}{6}x)+4(4) \\ \\ (\frac{5}{6}x+4)^2=\frac{25}{36}x^2+\frac{10}{3}x+\frac{10}{3}x+16 \\ \\ (\frac{5}{6}x+4)^2=\frac{25}{36}x^2+\frac{20}{3}x+16 \end{gathered}[/tex]So, the final answer is 25/36 x^2 + 20/3 x + 16.
