Eighth Day

Hi everyone! It was truly a winter wonderland this morning, but fortunately almost (if not) everyone were there in class. I am Rowsell by the way and I am going to summarize everything we learned in Pre- Cal today *i apologize if I'm not very specific (i'm more into numbers than words)*...
Firstly, in our morning class we continued discussing about Binomial Theorem and learned the formula, which is in the picture below along with the explanation:

*All the examples are those we did in class
Example 1: Expand and simplify using the binomial expansion:   

a) (3x - y) ⁵

Step #1: list the values Step #2: use the formula and plugged in values Step #3: Simplify Step #4: the answer

*Make sure you check everything before moving on, especially the + and – signs, because they can be tricky sometimes ;)

*And remember (-3x) ⁰  isn’t the same as -3x⁰, because (-3x) ⁰ = 1 and -3x⁰= -3 (the brackets make a difference)

We also learned is to find a specific term within a binomial expansion we can expand the binomial until we locate the specific term or to make things a little simpler we can use the formula shown on the below:

Example 2: Using the formula for calculating specific term,find the following terms

 a) the 4^th term of (x - 2y)¹⁰

Step #1: list the values Step #2: use the formula and plugged in values Step #3: Simplify Step #4: the answer

Thankfully, we did not have any quiz in the afternoon and continued on where we left off in the morning...

Example 3: Find the coefficient of the term containing x¹⁸ if (2x - x²)¹¹ 

Step #1: list the values Step #2: Solve/ Look for k Step #3: use the formula and plugged in values Step #4: Simplify Step #5: the answer

Lastly, we learned about finding the error in the binomial theorem:

Solve for the right answer, then look closely in the "SOLUTION WITH ERRORS" to find the error that was made

Near the end of class, we received an assignment consisting all the things we did/ learned in class about Binomial Theorem