Write the product as linear factors: (x^2−4)(x^2−9)
The product as linear factors can be written as:
(x + 2)(x - 2)(x + 3)(x - 3)
To write the product (x^2-4)(x^2-9) in linear factors, we can use the difference of squares and difference of cubes formulas.
First, let's factor x^2 - 4. This is a difference of squares, which can be factored as (x - 2)(x + 2).
Next, let's factor x^2 - 9. This is a difference of squares, which can be factored as (x - 3)(x + 3).
Now, we can write the original expression as the product of these linear factors:
(x^2 - 4)(x^2 - 9) = (x - 2)(x + 2)(x - 3)(x + 3).
So, the product (x^2 - 4)(x^2 - 9) can be written as (x - 2)(x + 2)(x - 3)(x + 3).