Question

How do you factor `u^2 - 16v^2`?

Answer 1

This is a difference of squares:

`u^2-16v^2 = u^2 - (4v)^2 = (u-4v)(u+4v)`

Explanation:

In general `a^2 - b^2 = (a-b)(a+b)`

Putting `a=u` and `b=4v` we have

`u^2-16v^2 = u^2 - (4v)^2`

`= a^2-b^2 = (a-b)(a+b)`

`= (u-4v)(u+4v)`