Bianca has a large beach towel measuring 16 feet by 28 feet. How can she use the difference of two squares to find the area of the beach towel? Select from the following expressions.

Question

Responses

222−162
22 squared minus 16 squared

282−162
28 squared minus 16 squared

222−62
22 squared minus 6 squared

282−62

Answer 1

To find the area of Bianca's large beach towel using the difference of two squares, we need to recognize that the area \( A \) of a rectangle can be expressed as the product of its length and width. In this case, the beach towel measures 16 feet by 28 feet, so the area is:

\[ A = 16 \times 28 \]

The difference of two squares formula is given by:

\[ a^2 - b^2 = (a - b)(a + b) \]

We can express the area calculation in a way that allows us to use this formula. To do this, we can rewrite \( 28 \) as \( 22 + 6 \) and \( 16 \) as \( 22 - 6 \):

• Set \( a = 28 \) and \( b = 16 \) gives us \( 28^2 - 16^2 \).

Using the formula for the difference of squares:

\[ 28^2 - 16^2 = (28 - 16)(28 + 16) \]

Therefore, the correct expression that uses the difference of two squares to find the area of the beach towel is:

28 squared minus 16 squared (which corresponds to the expression \( 28^2 - 16^2 \)).