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

Question

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Answer 1

To factor the product (x^2 - 4)(x^2 - 9) as linear factors, we first look for common factors and then use difference of squares.

(x^2 - 4) can be factored as (x + 2)(x - 2) since it is a difference of squares:

(x^2 - 4) = (x^2 - 2^2) = (x - 2)(x + 2)

Similarly, (x^2 - 9) can be factored as (x + 3)(x - 3) since it is also a difference of squares:

(x^2 - 9) = (x^2 - 3^2) = (x - 3)(x + 3)

Therefore, the product (x^2 - 4)(x^2 - 9) can be written as:

(x + 2)(x - 2)(x + 3)(x - 3)