Question

Write the product as linear factors: (x2−4)(x2−9)
.(1 point)

Answer 1

To express the product \((x^2 - 4)(x^2 - 9)\) as linear factors, we need to factor each quadratic expression.

1. **Factor \(x^2 - 4\)**:
\[
x^2 - 4 = (x - 2)(x + 2)
\]
(This is a difference of squares.)

2. **Factor \(x^2 - 9\)**:
\[
x^2 - 9 = (x - 3)(x + 3)
\]
(This is also a difference of squares.)

Now, we can combine the factors from both expressions:
\[
(x^2 - 4)(x^2 - 9) = (x - 2)(x + 2)(x - 3)(x + 3)
\]

Thus, the product \((x^2 - 4)(x^2 - 9)\) expressed as linear factors is:
\[
(x - 2)(x + 2)(x - 3)(x + 3)
\]