HOW TO BE SICK AT PRECAL (The Binomial Theorem)

Hello my name is Marc. I will be teaching you about The Binomial Theorem.

The Binomial Theorem is when you expand the powers of binomials.

You can easily expand them by using Pascal's Triangle shown here:

Every time the power of a binomial increases you go down the triangle.

The sum of the exponent in each term equals to the power of the binomial expansion. 

The X variable begins with the same value as the power of the binomial and decreases by one in each successive term. 

The Y variable appears in the second term of the expansion and increases by one until it matches the power of the binomial.

The numbers of terms in the expansion contain N + 1 terms in the expansion.

The coefficients of the binomials are the combinations of the power number beginning with nCo and ending at nCn and are symmetrical.

These are important rules you should remember:

1. A binomial expansion where the exponent is n will have a n + 1 terms when expanded.

2. A binomial expansion where the exponent is even will have an odd number of terms when expanded causing the expansion to have a middle term.

3. A binomial expansion where the exponent is odd will have an even number of terms when expanded causing the expansion to not have a middle term. 

4.If a pattern occurs like 5C1=5C4 and 4C0=4C4 and 3c1=3C2 you will not have to calculate all combinations.

I CHOOSE DANIEL :) ok bye.