Pre calc 12 help

Question

given f(x)=x^2-9 and g(x) = x^2+3x-1, find (fg)(x) 

Answer 1

The functions are f (x ) = x ² - 9  and g (x ) = x ² + 3x - 1 

(f g )(x ) = f (x ) * g (x )

              = (x ² - 9)(x ² + 3x - 1)

              = x ² (x ² ) + x ²(3x ) + x ²(-- 1 ) - 9 (x ²) - 9(3x ) - 9( - 1)

             = x ⁴ + 3x ³ - x ² - 9x ² - 27x + 9

             = x ⁴+ 3x ³ - 10x ² - 27x  + 9

(f g )(x )  = x ⁴+ 3x ³ - 10x ² - 27x  + 9