Multiplying Binomials
Area of a Window
The diagram at the right shows the basic dimensions for a window. The glass portion of the window has a height-to-width ratio of 3 : 2. The framework adds 6 inches to the width and 10 inches to the height.
a. Write a polynomial expression that represents the total area of the window, including the framework.
b. Find the area when x = 10, 11, 12, 13 and 14.
SOLUTION
a) Verbal Model:
Total Area = Height of window Width of window
Total Area = A (square inches)
Height of window = (inches)
Width of window = (inches)
Algebraic Model:
Area model
FOIL pattern
Combine like terms
b
You can evaluate the polynomial expression by substituting x-values. For instance, to find the total area of the window when , substitute 10 for x.
The areas for all five x-values are listed in the table.
