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

Question

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