![area models area models](https://showme0-9071.kxcdn.com/files/78972/pictures/thumbs/552185/last_thumb1354913720.jpg)
I wrote it out a little differently in the FOIL process but this is the same answer you would have gotten in using FOIL.
Area models plus#
I could do the product x+3 times 2x+1 by writing its rectangle I'm going to call this top x+3 notice my drawing isn't to scale but that's okay I'm just going to have my products be in here, 2x+1 it's going to be my side lengths, so now when I multiply each of these four things and add them together I'll get the same answer that I would have gotten had I foiled, here's what I mean, x times 2x is 2x squared, 3 times 2x is 6x, x times 1 is x, 3 times 1 is 3, so when I add all those together I'll get 2x squared plus,6x plus x, is 7x plus 3 that's the answer for this product. So what that means is that I can use this idea of broken rectangles to multiply binomials. Here is what I mean, 4x1 give me this little area 4x1 is 4, 3x1 is 3, 4x5 will be 20, 3x5 is 15, I broke this into four separate pieces and when I add them up I'll get 42.
![area models area models](https://i0.wp.com/youvegotthismath.com/wp-content/uploads/2017/05/area-model-pin.jpg)
You would get that same answer if I broke that rectangle into pieces, instead of 7 I'm going to break it into 4 and 3, 4+3 is 7, and on the side here I'm going to make it 1+5, now I have four different rectangles and when I find the area of each little chunker, you'll see they add up to 42.
![area models area models](https://mr-trex.weebly.com/uploads/3/9/9/5/39956389/6531024_orig.png)
Like if I had this rectangle here and I told you the top was 7 the side was 6 you would say area equals 7圆 or 42. Let me show you what I mean, you guys already know about area, if you have a rectangle the area of the rectangle is length times width. When you're multiplying polynomials, really what you're doing is using the distributive process but a lot of times you're using it multiple times over each term and each polynomial gets multiplied by everything else it gets really tricky that's why a lot of times teachers will show students what I'm going to show you here it's the area model for multiplying polynomials.