Multiplying Polynomials

Question

A rectangle has a base of (4x +2) and a height of (2x + 3). What is the area?

Answer 1

The formula for the area of a rectangle:

Area = Base * Height

As such, your area will be (4x + 2) * (2x + 3).

However, we need to multiply this out. This will require the use of the Distributive Property. We want to multiply each item in the first parentheses with each item in the second parentheses. Then, we will add all the terms up.

The items in the first parentheses: 4x and 2

The items in the second parentheses: 2x and 3

So we need to multiply

4x * 2x

4x * 3

2 * 2x

2 * 3

and we get

4x * 2x = 8x²

4x * 3 = 12x

2 * 2x = 4x

2 * 3 = 6

Let's add up all of our results!

8x² + 12x + 4x + 6 = 8x² + 16x + 6

Answer 2

Recall that the formula for area of a rectangle is: A = lw (otherwise known as base and height)

In this case we are given both of the variables on the right. By substituting those given values, we get:

A = (4x + 2)(2x + 3)

Now, in order to determine the area, we need to multiply the binomials. Perhaps you've learned FOIL or heard of it. Multiply each term in the first binomial by each in the second.

8x² + 12x + 4x + 6

Next, we will combine like terms. The result is:

8x² + 16x + 6 units² (unless specific units were provided)