Question

The area of a square can be represented by the trinomial 9x^2 - 54x + 81. Which of the following is the length of one side of the square?
*free response question

Answer 1

$Use\ (a-b)^2=a^2-2ab+b^2\\\\9x^2-54x+81=\underbrace{(3x)^2-2(3x)(9)+9^2}_{(*)}=(3x+9)^2\\\\\text{The formula of an area of a square with a side x:}\ A=x^2.\\\\\text{Therefore we have answer:}\ The\ length\ of\ side\ of\ the\ square\ is\ 3x+9.$