These have to do with binomial expansion please answer all of the questions and please show your work so it is easier to understand.

1) Determine the number of terms there are in the expansion of (a+b)

2)Determine the number of terms there are in the expansion of (a+b)⁹

3)Determine the number of terms there are in the expansion of (a+b)⁵

4)Determine the number of terms there are in the expansion of (a+b)¹⁹⁹⁹

5)Determine the number of terms there are in the expansion of (a+b)³⁹

6)Expand the given binomial. Each term(include the sign if it is negative)goes in a separate answer box.

Expand (1-x)⁸

1st term:

2nd term:

3rd term:

4th term:

5th term:

6th term:

7th term:

8th term:

9th term:

7)Expand the given binomial. Each term(include the sign if it is negative)goes in a separate answer box.

Expand (x³ +1)⁵

1st term:

2nd term:

3rd term:

4th term:

5th term:

6th term:

8)Expand the given binomial. Each term(include the sign if it is negative)goes in a separate answer box.

Expand (1+x)⁷

1st term:

2nd term:

3rd term:

4th term:

5th term:

6th term:

7th term:

8th term:

9)Expand the given binomial. Each term(include the sign if it is negative)goes in a separate answer box.

Expand (2x-1/2y)⁴

1st term:

2nd term:

3rd term:

4th term:

5th term:

10)Expand the given binomial. Each term(include the sign if it is negative)goes in a separate answer box.

Expand (2x-y)⁴

1st term:

2nd term:

3rd term:

4th term:

5th term:

11)Expand the given binomial. Each term(include the sign if it is negative)goes in a separate answer box.

Expand (x+2y)⁶

1st term:

2nd term:

3rd term:

4th term:

5th term:

6th term:

7th term:

12)Expand the given binomial. Each term(include the sign if it is negative)goes in a separate answer box.

Expand (x/2-y/3)⁴

1st term:

2nd term:

3rd term:

4th term:

5th term:

13)Expand the given binomial. Each term(include the sign if it is negative)goes in a separate answer box.

Expand (1-5m)⁵

1st term:

2nd term:

3rd term:

4th term:

5th term:

6th term:

14)Determine the coefficient of the term that contains x⁸ in (x+y)¹⁵

15)Determine the coefficient of the term _nC_pa⁴b¹⁶ from the expansion of (a+b)²⁰

16)Determine the coefficient of the term _nC_pa¹⁰b¹⁰ from the expansion of (a+b)²⁰

17)Determine the coefficient of the term _nC_pa¹²b⁸ from the expansion of (a+b)²⁰

18)Determine the coefficient of the term _nC_pa¹⁸b² from the expansion of (a+b)²⁰

19)Determine the third term (3x-2y)⁵

20)Determine the seventh term of (a+b)¹⁰

21)Determine the fifteenth term of (x-y)²⁰

22)Determine the fifth term of (2x+3y)⁷

23)Determine the fourth term of (2a²-3xy³)⁶

24)Determine the sixth term of (a-b)¹⁴

25)Determine the fourth term of (x+3y)⁸