Bionomial Theorem

Question

Which term of the expansion of (x+5)^8 contains x^7

Term number   

Answer 1

(x+5)^8

has 9 terms

1st is x^8

2nd is 8x^7(5)

3rd 28x^6(5^2

4th 56x^5(5^3)

5th 56x^4(5^4)

6th 28x^3(5^5)

7th 8x^2(5^6)

8th x(5^7)

9th 5^8

each term is 8Cr(x^r)(5^(8-r) where 8Cr = 8!/r!(8-r)! as r goes from 1 to 8

or use the last line below of Pascal's triangle

1

11

121

1331

14641

15101051

1615201561

1721352171

182856562881

Answer 2

The first term of the expansion is x⁸.

The second term of the expansion is x⁷.