2. FOIL
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Assign a variable for the expression.
Use the Distributive Property.
Use the expression for the area you got in Part B.
a+3 and a+5
a^2+8a+15
71 square feet
Let's introduce variables so we can use algebra to work out the answers.
| Description | Variable |
|---|---|
| Side length of the current square shaped office. | a |
| Width of the new rectangular office. | w |
| Length of the new rectangular office. | l |
We are given information on how the dimensions of the office will be changing. Let's express this information in terms of the variables.
| Description | Expression |
|---|---|
| The new office is 3 feet wider than the old office. | w=a+3 |
| The new office is 5 feet longer than the old office. | l=a+5 |
The area of a rectangle is the product of its length and width. Let's use the expressions from Part A to find this product. We can use the Distributive Property to find the polynomial expression, which is the product of the two binomials.
The area of Monica's new office in terms of the side length of her current square-shaped office is a^2+8a+15 square feet.
We can substitute a=7 into the expression we got in Part B to find the area of Monica's new office.
The area of Monica's new office is 120 square feet. To find the difference compared to the current office space, we need to subtract. Note that her current office is a square, so it's area is 7^2=49 square feet. Expansion:120-49=71square feet