Question

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

a) (x + 2)(x + 3)(x - 2)(x - 3)
b) (x + 2)(x - 2)(x + 3)(x - 3)
c) (x + 4)(x - 4)(x + 9)(x - 9)
d) (x - 4)(x + 4)(x - 9)(x + 9)

Answer 1

To write the product of (x^2 - 4)(x^2 - 9) as linear factors, we expand the expression and use the difference of squares formula to obtain the correct answer as (x + 2)(x + 3)(x - 2)(x - 3).

Step-by-step explanation:

To write the product of (x^2 - 4)(x^2 - 9) as linear factors, we can expand the expression and look for common factors. Firstly, we can use the difference of squares formula to expand (x^2 - 4) as (x + 2)(x - 2), and (x^2 - 9) as (x + 3)(x - 3). Multiplying these two expressions together, we get (x + 2)(x - 2)(x + 3)(x - 3). Therefore, the correct answer is option a) (x + 2)(x + 3)(x - 2)(x - 3).