Trinomials are expressions that have three terms and highest power of 2
The expression [tex]\big(\frac{2}{3}x+3\big)^2[/tex] as a trinomial in its simplest form is [tex]\frac{4}{9}x^2 + 4x+9[/tex]
The factored function is given as:
[tex]\big(\frac{2}{3}x+3\big)^2[/tex]
Expand the above function
[tex]\big(\frac{2}{3}x+3\big)^2 = \big(\frac{2}{3}x+3\big) \times \big(\frac{2}{3}x+3\big)[/tex]
Factorize the expression above
[tex]\big(\frac{2}{3}x+3\big)^2 = \frac{2}{3}x(\frac{2}{3}x+3) +3(\frac{2}{3}x+3\big)[/tex]
Open brackets
[tex]\big(\frac{2}{3}x+3\big)^2 = \frac{4}{9}x^2 + 2x + 2x+9\big[/tex]
Evaluate like terms
[tex]\big(\frac{2}{3}x+3\big)^2 = \frac{4}{9}x^2 + 4x+9\big[/tex]
Hence, [tex]\big(\frac{2}{3}x+3\big)^2[/tex] as a trinomial in its simplest form is [tex]\frac{4}{9}x^2 + 4x+9[/tex]
Read more about trinomial at:
https://brainly.com/question/13136492
