Questions on Expansions

Question 21

Question:   Simplify the term independent of x in the expansion of

Answer:   

Question 22

Question:   Find the term independent of x in the expansion of

Answer:   


\There is no term containing x^o i.e., independent of x.

Question 23

Question:  

Answer:   

Question 24

Question:  

Answer:   





Note:

Question 25

Question:   Find the greatest term in the expansion of (2x + 3y)²⁸ when x = 9, y = 4.

Answer:   




The greatest value of 'r' can be 11.
Hence, the greatest term is the 12^th term.

Question 26

Question:  

Answer:   

Question 27

Question:   The first three terms in the expansion of (x + y)ⁿ are 1, 56 and 1372 respectively. Find the values of x and y.

Answer:   



But x = 1

Question 28

Question:   Using binominal theorem, show that

Answer:    i)

which is divisible by 64.
_ii)

which is divisible by 25.

Question 29

Question:  

Answer: