Question

write the product as linear factors \left(x^2-4\right)\left(x^2-9\right)

Answer 1

To write the expression \((x^2 - 4)(x^2 - 9)\) as linear factors, we first recognize that both \(x^2 - 4\) and \(x^2 - 9\) can be factored further.

1. Factor \(x^2 - 4\):
\[
x^2 - 4 = (x - 2)(x + 2)
\]

2. Factor \(x^2 - 9\):
\[
x^2 - 9 = (x - 3)(x + 3)
\]

Now, we can combine these factors:

\[
(x^2 - 4)(x^2 - 9) = (x - 2)(x + 2)(x - 3)(x + 3)
\]

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

\[
(x - 2)(x + 2)(x - 3)(x + 3)
\]