Multiplying monomials by polynomials: area model
About this video
A rectangle of height 4 is split into three smaller rectangles with widths x^2, 3x and 2. Finding each area (4x^2, 12x and 8) and adding them expresses the total area as the trinomial 4x^2 + 12x + 8.
You'll be able to
- find the area of a rectangle whose side is an algebraic expression.
- multiply a monomial by a number, such as 4 times 3x = 12x.
- add the areas of parts to write the total area as a trinomial.
Key words
- trinomial
- A polynomial with three terms, like 4x^2 + 12x + 8.
- area
- Height times width of a rectangle.
- area model
- A rectangle split into parts to show how multiplying works.
Transcript
- [Voiceover] We're asked to express the area of the entire rectangle below as a trinomial. We have our rectangle here and it's broken up into these three smaller rectangles. And we see for all of these rectangles, the height here is four units and then the widths are expressed in terms, or at least the first two, are expressed in terms of x and then this last one has a width of two.
So what's the area of the entire rectangle? I encourage you to pause the video and think about it. What's the area of this blue, this blue, it looks like a square, but let's just call it a rectangle, which all squares are rectangles so that's safe. Well, it's going to be the height times the width.
So the area here is going to be the height, which is four, times the width, which is x squared. And then to that, we want to add the area of this, I guess we could say this salmon colored rectangle and well that's going to be the height four times the width 3x.
So we could say four times 3x, we could write it like that, but what is 4 times 3x? Well, that's going to be 12x. You have 3x four times, I have 12 xs, so that's going to be 12x. 12x is the area of this salmon colored rectangle. And then, finally, the area of this green rectangle, we actually can figure out it exactly, we don't even have to express it in terms of a variable.
Its height is four, its width is two, so the area's going to be four times two, or eight. And we are done.
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