Given [tex]f(x) = x^2 + 6x + 9, g(x) = x^2 - 9[/tex]:
[tex](f+g)(x) = (x^2 + 6x+9)+(x^2-9) =2x^2+6x=2x(x+3)[/tex], which is the second expression
[tex](f-g)(x) = (x^2 + 6x+9)-(x^2-9) =6x+18=6(x+3)[/tex], which is the first second expression
[tex](fxg)(x) = (x^2+6x+9)(x^2-9) = (x^4-9x^2)+(6x^3-54x)+(9x^2-81)=x^4+6x^3-54x-81[/tex], which is the fourth expression
[tex](f/g)(x) = (x^2+6x+9)/(x^2-9) = \frac{(x+3)^2}{(x+3)(x-3)} = \frac{x+3}{x-3}[/tex], which is the third expression
