what to do with this math problem?

Question

Factor the following.

81-4r^2

 

the answer i gave was wrong. could someone please help me understand what to do?

Answer 1

81 - 4r²

 

Looking at this I note that what we actually

have is the difference of two squares.

81 = 9²

4r² = (2r)²

 

81 - 4r² = 9² - (2r)²

 

There is a formula for factoring the difference of two squares.

a²-b² = (a-b)(a+b)

In this case we have a=9, b= 2r

 

81-4r² = (9-2r)(9+2r)