Answer:
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.
