The Binomial Theorem

How many terms are in this expansion? terms

16

What is the fifth term in the expansion of (3x - 3y)7?

76545

hat is the first term in this expansion?

B

Which row of Pascal's triangle would you use to expand (2x + 10y)15?

C

What is the coefficient of the x6y3 term in the expansion of (x + 2y)9?

D

Which of the following is the expansion of (2m - n)7?

E

Without actually writing the formula, explain how to expand (x + 3)7 using the binomial theorem.

To write the coefficients of the 8 terms, either start with a combination of 7 things taken 0 at a time and continue to 7 things taken 7 at a time or use the 7th row of Pascal's triangle. For the first term, write x to the 7th power and 3 to the 0 power. Then decrease the power on x and increase the power on y until you reach x to the 0 and y to the 7. Simplify by evaluating the coefficients and powers of 3.