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

Answer 1

To write the expression \((x^2 - 4)(x^2 - 9)\) as linear factors, we first need to factor each quadratic term separately.

1. The first term \(x^2 - 4\) is a difference of squares: \[ x^2 - 4 = (x - 2)(x + 2) \]

2. The second term \(x^2 - 9\) is also a difference of squares: \[ x^2 - 9 = (x - 3)(x + 3) \]

Now we can combine these factors: \[ (x^2 - 4)(x^2 - 9) = (x - 2)(x + 2)(x - 3)(x + 3) \]

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