How do you factor this into a polynomial?

Question

A manufacturer of metal washers needs to determine the cross-sectional area of each washer. If the outer radius of the washer is R and the radius of the hole is r, express the area of the washer as a polynomial. Factor this polynomial completely.

Answer 1

The hole of the washer will never have an area because it does not occupy any surface of the object. 

 

The area of any circle is πr².  To find the area of this washer, we take the area of the outer circle minus the area of the inner circle (the hole).

 

A = πR² - πr²

 

A = π(R² - r²)

 

The term (R² - r²) is a difference in perfect squares.

 

A = π(R + r)(R - r)

Answer 2

A washer is a disk with a hole drilled through the middle of it.  

 

Cross sectional area of the washer = 

 

       Area of disk - Area of drilled out portion = πR² - πr²

 

                                                                             = π(R² - r²)

 

                                                                             = π(R - r)(R + r)