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Binomial Products (Multiplying/Expanding)

Example of a binomial product on a chalkboardMultiplication is one of the most basic of operations.

When it is applied to numbers it takes us some time (as young students) to learn the algorithms/methods involved.  This is equally true of multiplying algebraic expressions.  Mathematicians had to work out the best way of writing and understanding the symbols.  They then had to work out how to perform multiplications so that they gave consistent and correct answers.  You are walking in their footsteps.

I know that a lot of students struggle with this skill, but it may comfort you to know that no one, not even the greatest geniuses in history, were born knowing this skill.  Everyone has to learn it for the first time.  It just takes some determination and practice … but it certainly helps to have some understanding of what you are doing, and why.

I will be trying to share these insights with you as I show you what to do.

In time, I hope you grow to love algebra as I do (much as I like literature, music or art).  It is simply a form of expression, a dance of ideas, a pattern of concepts!

A Mathematical Pun ~ Explaining Binomial Products

One of the fundamental skills of algebra is being able to multiply larger expressions.  Here, I explain one of the most common of these structures ... how to multiply two terms by two terms.

Mathematically, we call this "multiplying a binomial by a binomial" or, simply, "a binomial product."

Before you turn away in disgust :-), let me encourage you to watch the video ... whether you already know how to do this, or not!  There is something here for everyone.

If you are not good at algebra and do not understand the process (or do not care), you will learn why you have been performing this skill with great regularity all your life ... it is very natural.  I actually speak about what happens at children's birthday parties.

If you are good at algebra and already know how to do this, you will be entertained with a mathematical pun.  On second thoughts, maybe it will make you groan :-) ... but I think it will be worth a few minutes of your time.

Either way, I hope you enjoy the video!

I enjoyed your presentation and no it wasn’t too long. Each subtraction algorithm has its merit as you demostrated, but after learning the “one up and one down” method, I’m employing it because of its speed and ease of usage. Even my wife, who hates mathematics with a passion, thinks it’s too easy. I look forward to your future presentations on both multiplication and number theory. I read an introduction text book some twenty five years ago on number theory by Oystein Ore who taught at Yale for better than twenty years. So in closing, please produce these lectures and the longer the better. Thanks.
Dennis Bell (on a CCM YouTube video about How to Subtract (Large) Numbers Easily)

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