## How to multiply binomials using a box!

Wednesday, February 10th, 2010Many people find this more visual and intuitive than FOILing.

I split the video into 8 brief parts. Each part features one practice problem, fully explained and demonstrated on the whiteboard.

If you, your family, or your friends would like to see me make an instructional video about a particular math topic or type of problem, leave a comment to nominate your math problem for its very own video!

And if you like the video, please feel free to click on the “heart” to show that you “heart” it. <3

#1 – Multiplying Binomials with the Box Method (alternative to FOILing) from Rebecca Zook on Vimeo.

Click on “more” for the other parts of the video — four more examples, extra practice problems for you to test your mastery of FOIL, and answers to the extra practice problems!

#2 – Multiplying Binomials with the Box Method (alternative to FOILing) from Rebecca Zook on Vimeo.

#3 – Multiplying Binomials with the Box Method (alternative to FOILing) from Rebecca Zook on Vimeo.

#4 – Multiplying Binomials Using the Box Method – extra problems for you to practice with on your own from Rebecca Zook on Vimeo.

Multiplying Binomials with the Box Method – #5 – check your answer to the first practice problem from Rebecca Zook on Vimeo.

Multiplying Binomials with the Box Method – #6 – check your answer to the second practice problem from Rebecca Zook on Vimeo.

Multiplying Binomials with the Box Method – #7 – check your answer to the third practice problem from Rebecca Zook on Vimeo.

Multiplying Binomials with the Box Method – #8 – check your answer to the fourth practice problem from Rebecca Zook on Vimeo.

*If you’re visiting from Mathematics and Multimedia Math Carnival No. 4, welcome! I’d love to hear what you think of this video! (If you haven’t heard about the Mathematics and Multimedia Math Carnival, check it out – here’s the homepage run by Guillermo Bautista, and the fourth edition was hosted by Wild About Math!) *

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These videos are great! I’m so glad to see an alternative to FOIL as it is a limited use concept. You’ve explained things so well and I love the visual style.

Wish I had seen this before I blogged about our FOIL video.

http://blog.thinkwell.com/2010/07/prealgebra-multiplying-binomials.html

April, it’s so nice to “meet” you! Thanks for stopping by. I’m really excited to share this idea because I think it’s an easier way for some people to learn how to multiply binomials. Thanks for sharing your blog post, too!

Thank you so much for showing me another alternative to foiling! Thease videos are wonderful. I appreciate you for helping me understand better. You explain math so well.

You are soooooooooo welcome!!!

Rebecca – I’m so relieved to see that you are presenting other ways of understanding the distributive property than the FOIL method, which does not work well for multiplying polynomials with more than 2 terms. Unfortunately, the box method becomes nothing more than a magic trick (much like the FOIL method) if it is presented without associating it with area. The only reason that we know that the left side of the equation is actually equal to the right side is because they are both respresentations of the AREA of the SAME box.

For example: (x+2)(x-7)=x^2-7x+2x-14 BECAUSE

if I label the width of the box as x+2 and the length of the box with x-7 then one way to express the area of the box is

Area=length*width=(x+2)(x-7). I can also calculate the area of the larger box by finding the area of each of the smaller boxes and adding them up. This gives me the expression on the right side of the equation above. We can only conclude that these two expressions are EQUAL because they represent the area of the same box. Without that critical piece of information, there’s no good reason that these two expressions SHOULD be equal.

(PS I teach math everyday at a community college in Oregon – good job overall 🙂

Kari, thanks so much for your superthoughtful comment! Wow, I totally neglected to mention area in the video, and you’re right, it needs to be in there! I will definitely incorporate your feedback into future versions. Thanks for your comment, and it’s nice to “meet” you here! 🙂

there is another method for doing binomials that is not the box or the foil method but I do not know the name of it. Would you be able to tell me the name ? It goes like

x – 8

x – 3

———–

– 3x + 24

x² – 8x

————–

x² – 11x + 24