What is the expression that represents the area of the rectangular garden? Explain your reasoning.

Question

The length of a rectangular garden is represented by (x - 5) meter and the width is represented by (x + 2) meter, Jim decided to cover all the area with grass.

Solve this using FOIL.

Explain the steps you used.

Answer 1

Hello, let's review the FOIL method to begin.

F: First (multiply the first terms in each binomial)

O: Outer (multiply the first term of the first binomial and the second terms of the second binomial)

I: Inner (multiply the two inner terms)

L: Last (multiply the second terms in each binomial)

When multiplying binomials, we use FOIL to make sure we multiply the terms in each binomial appropriately. How does this relate to your problem? Since we want to cover the total area of grass, we must find the area of the garden. What is the formula for Area?

A = length x width

Let's fill in the length and width with the expressions given to us in the problem. L = (X-5) and W = (x+2).

A = (x-5)(x+2)

Now, we have a binomial multiplication to do. We can use FOIL as shown below.

A = (x-5)(x+2) <--- F: x*x= x² ; O: x*2= 2x ; Inner: -5*x = -5x ; Last: -5*2 = -10

A = x² + 2x - 5x -10

Combine Like Terms: 2x - 5x = -3x

A = x² - 3x -10