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Multiplying Polynomials using Area Models  Problem 1
Alissa Fong
Alissa Fong
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
Here I’m given 2 binomials multiplied together. So in order to do this problem, I could use FOIL, but this problem asks me use an area model.
So I’m going to draw a rectangle that’s 2 by 2 to represent binomial times binomial. Then across the top I’m going to write my first one 3x plus 1, down the side I’m going to write my second one x take away 2, and this is a little tricky because some of you guys are thinking you can’t have a negative area and that is a little weird because when we fill in these boxes, you’re going to see we’re going to get a negative quantity in one of them and that’s weird like area can’t be negative. That’s why this concept has a little bit of a trick in your brain. You just got to make sure you’re keeping track of the positive and negative signs and trust that the process works for multiplying binomials.
3x plus 1 I wrote across the top x minus 2 and down the side, so here 3x times x inside this box I’m going to have 3x². Here I’m going to do 1 times x to give me this plain old 1 x. Here 3x times 2 is 6x and then here I’ll have 2. It’s kind of weird because they’re negative areas. I’m just using this idea to help me find the product.
Last thing is to combine like terms, 3x², here I have 6 and 6x, excuse me I have x and 6x, those can be combined to 5x take away 2, that’s my final answer that I would have gotten through Foiling, I just wrote out in a different way. So this Area Model can be really useful because it helps you organize each of your different products for multiplying in these polynomials.
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Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
Sample Problems (4)
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Multiplying Polynomials using Area Models
Problem 1 6,331 viewsMultiply (3x + 1)(x − 2) using an area model.

Multiplying Polynomials using Area Models
Problem 2 4,775 viewsMultiply:
(2x − 4)(3x² + 5x − 6) 
Multiplying Polynomials using Area Models
Problem 3 4,537 viewsMultiply:
(a² + 2a + 3)(a² − 4) 
Multiplying Polynomials using Area Models
Problem 4 1,091 views
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