1. HSAATH – Special Cases when working with Polynomials Tuesday, Oct. 22nd

2. Special Case 1 – Squaring Binomials Squaring a binomial is not that tough. It just means to multiply the binomial by itself, using the regular strategies for multiplication. However, it sure is nice when you can spot a shortcut! Look at the following problems and final answers. Do you spot a pattern? How does the first term in the answer relate to the problem? How does the last term in the answer relate to the problem? How does the middle term relate to the problem?

3. Special Case 1 Well, 10 is 52 and 25 = 5 2. Well, 6 is 32 and 9 = 3 2. Well, -6 is -32 and 9 = (-3) 2. Well, -14 is -72 and 49 = (-7) 2. See the pattern now? Look at a few more problems. Do the patterns you found before still work? What about that middle term?

4. Special Case 1 When you square a binomial, you get the following: (A + B) 2 = A 2 + 2AB + B 2 (A – B) 2 = A 2 – 2AB + B 2 The A and B are squared to create the first and last terms of the answer. Twice the product of A and B form the middle term!

5. Special Case 2 – Multiplying Sums and Differences Let’s play “Spot the Pattern” here also. Look at the problems and the solutions. What makes the problems special? How does that “specialness” translate into the final answer? Did you spot it? Write out what is happening! When you multiply together binomials whose signs are opposites, you will get a difference of two squares as a result.

6. Special Case 3: Cubing a Binomial Cubing a binomial is like squaring in that there is a long way and a short way to achieve the final expression. Long way – write it out and use FOIL a lot. Not all that hard to do, just long.

7. Special Case 3 The short way requires you to memorize a formula. To cube a binomial….. Let’s see an example of what this means. For this example, A = 2x and B = -3. Plug those expressions into the formula and simplify.