Write the product as linear factors: (x^2 - 4)(x^2 - 9)

Answer 1

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

1. The expression \(x^2 - 4\) is a difference of squares, which can be factored as: \[ x^2 - 4 = (x - 2)(x + 2) \]

2. The expression \(x^2 - 9\) is also a difference of squares, and can be factored as: \[ x^2 - 9 = (x - 3)(x + 3) \]

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

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