Addition & Subtraction
Problem Solving
Using Addition or Subtraction of Polynomials
An application of polynomials is their use in finding areas of a geometric object. In the following examples, we will see how the addition or subtraction of polynomials might be useful in representing different areas.
Example 1 Write a polynomial to represent the area of the figure.
This shape is formed by two squares and two rectangles.
The blue square has area: y · y = y2. The yellow square has area: x · x = x2.
The pink rectangles each have area: x · y = xy.
To find the total area of the figure we add all the separate areas.
Total area = y2 + x2 + xy + xy = y2 + x2 + 2xy