Question

Find the 7th term of the expansion of (3c + 2d)^9.

a.
760c^3d^6

c.
145,152c^3d^6

b.
760c^4d^5

d.
145,152c^4d^5

Answer 1

c

Explanation:

Using Pascal's triangle, the expansion, although EXTREMELY lengthy, will help you find the 7th term. I am going to type out the expansion only up til the 7th term (although there are actually 10 terms because we are raised to the power of 9). If you would like to learn how to use Pascal's Triangle for binomial expansion, you will need to visit a good website that explains it because it's just too difficult to do it via this website.

The expasion is as follows (up to the 7th term):

`1(3c)^(9) +9(3c)^(8)(2d)^(1) +36(3c)^(7)(2d)^(2) +84(3c)^6(2d)^3+126(3c)^5(2d)^4+126(3c)^4(2d)^5+84(3c)^3(2d)^6`

That last term is the 7th term. You find out its value by multiplying all the numbers together and adding on the c^3d^6. Again those come from Pascal's triangle, and it's one of the coolest math things ever. I encourage you to take the time to explore how it works.