Algebra: More Common Products
More Common Products
In this algebra video tutorial, I demonstrate four more polynomial product formulas and how to derive them. These four formulas, along with the prior three formulas, should give some hint at the more general formulas of this type that will be derived later on. The derivations of the formulas are given in greater detail here, and you should read through them at your own pace.
Since I did not give polynomial substitution examples for the difference of cubes and the sum of cubes formulas in the video, I will go through those two examples below.
For the difference of squares, I will use the substitutions a = 3x and b = 4. I begin with the factored form with the way that it would probably look in a typical problem. Then I put it into the more recognizable factor form to make the substitutions more obvious. For the second equality, I apply the formula with the substitutions. Finally, I multiply the terms out to get the result.
For the sum of squares, I will use a = 2y and b = z. Again, I start with the factored form in its more natural state. Then to make the substitution apparent, I group the 2y terms. To get the equality on the second line, I apply the sum of cubes formula with the substitution. Finally, I simplify the product to get the result.
These substitutions are intended to give a more realistic look at how the formulas will be applied. I recommend trying a few more substitutions to get a better feeling for the formulas. Also, look and see if you can detect any patterns that are common between these formulas and the three formulas that I called Common Products.