How do you use the binomial series to expand # (2a-b)^7#?
The binomial theorem shows up in Pascal’s triangle (start with 1’s and then add adjacent numbers to find the number below):
Since we are taking this binomial to the 7th power, we have to look at the 7th row (where the single 1 on top is considered our 0th row) to find our coefficients.
Our coefficients are:
The two terms in the binomial are:
I have to multiply these terms together with the coefficients so that
Now we have to simplify: