Lesson 4 Summary

 

Expanding a binomial by multiplying is a very tedious process for any exponent larger than 3. It is possible to use patterns to help simplify this process. The exponents of the expansion follow an ascending and descending pattern, while the coefficients of the expansion can be found using Pascal’s triangle.

 

Determining the values of Pascal’s triangle for large exponents would take a long time, so combinations are used to determine entries of Pascal’s triangle to simplify this process. The generalized result is the binomial theorem:

 

 

 Any term of the expansion can be determined using the formula tk + 1 = nCk (x)n − k (y)k.