Write the product as linear factors: (x^2-9)(x^2-16)

Answer 1

To express the product $(x^2-9)(x^2-16)$ as linear factors, we first recognize that both $x^2-9$ and $x^2-16$ can be factored using the difference of squares formula:

1. $x^2-9=(x-3)(x+3)$
2. $x^2-16=(x-4)(x+4)$

Now, we can substitute these factorizations back into the original expression:

$$(x^2-9)(x^2-16)=[(x-3)(x+3)][(x-4)(x+4)]$$

Next, we can combine all the factors together:

$$(x-3)(x+3)(x-4)(x+4)$$

Thus, the complete product expressed as linear factors is:

$$(x-3)(x+3)(x-4)(x+4)$$