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 need to factor each quadratic expression.

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

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

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

Combining all factors, the complete factorization is: \[ (x - 2)(x + 2)(x - 3)(x + 3) \]

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