If f (x) = x2 - 81 and g (x) = (x - 9) - 1 (x + 9), find g (x) · f (x).

x^2 - 6561

Step-by-step explanation:

We are given f (x) = x^2 - 81 and g (x) = - 1 (x-9) (x+9), and are asked to find the product of these numbers. We could go about this in two different ways: distribute x^2 - 81 to - 1 (x-9) (x+9),

(x^2 - 81) (-1 (x-9) (x+9)) = x^4 - 6561

OR we can multiply out g (x), obtaining - x^2 + 81. With this, we can then simply multiply both functions:

(x^2 - 81) (x^2 + 81) = x^4 - 6561

I suggest doing the second method. In this method, we can see that the two have the difference of squares property. With this, when the expression is multiplied, we get:

x^4 - 81x + 81x - 6561.

Since the expression is difference of squares, we can go straight to x^4 - 6561 without having to distribute the 81's.