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In this lesson, we will learn how to find a specific term inside a binomial expansion and find the relation between two consecutive terms.

Q1:

Find the third term in the expansion of ( 4 π₯ + 3 ) 3 .

Q2:

Find the value of π₯ that satisfies

Q3:

Consider the expansion of ( 1 + π₯ ) π in ascending powers of π₯ . Given that the coefficient of π₯ 1 4 is equal to the coefficient of π 1 8 , determine the value of π .

Q4:

Find π 4 in the expansion of οΏ 5 β π₯ + β π₯ 5 ο 9 .

Q5:

Find π 3 in the expansion of οΏ 2 β π₯ + β π₯ 2 ο 1 3 .

Q6:

Find the third term in the expansion of οΏ 2 π₯ + 5 β π₯ ο 5 .

Q7:

Find π π + 3 in the expansion of οΌ 9 π₯ β 1 π₯ ο 8 3 π + 9 .

Q8:

Find π π β 3 in the expansion of οΌ 3 π₯ β 1 π₯ ο 2 4 π + 9 .

Q9:

If the coefficient of the third term in the expansion of οΌ π₯ β 1 4 ο π is 3 3 8 , determine the middle term in the expansion.

Q10:

If the ratio between the fourth term in the expansion of οΌ π₯ + 1 π₯ ο 9 and the third term in the expansion of οΌ π₯ β 1 π₯ ο 2 8 equals 7 βΆ 1 2 , find the value of π₯ .

Q11:

Consider the binomial expansion of ( 1 + π₯ ) π in ascending powers of π₯ . Given that π = π 8 6 when π₯ = 1 β 5 , find the value of π .

Q12:

In the binomial expansion of ( 1 + π₯ ) π , π is a positive, whole number and π π is the π th term, or the term which contains π₯ π β 1 .

If 8 ( π ) = 2 7 π Γ π 6 2 4 8 , what is the value of π ?

Q13:

Find the coefficient of π 5 in the expansion of ( 9 π₯ + 2 ) 6 .

Q14:

Find the coefficient of π 3 in the expansion of ( 1 4 π₯ + 3 ) 3 .

Q15:

Find the third term in the expansion of ο½ π + π π ο 1 9 1 1 1 4 1 9 β 2 8 .

Q16:

Consider the binomial expansion of ( 2 π₯ β π¦ ) 9 in ascending powers of π₯ . What is the seventh term?

Q17:

In a binomial expansion, where the general term is 1 5 π 1 8 β 9 π πΆ π₯ , determine the position of the term containing π₯ 9 .

Q18:

Find π 4 in the expansion of οΌ π₯ + 1 π₯ ο 1 4 .

Q19:

Let π π be the π t h term in the expansion of ( 1 + π₯ ) 3 4 in increasing powers of π₯ . Find all nonzero values of π₯ for which 2 π = π + π 2 1 2 0 2 2 .

Q20:

Given that the sum of the first, middle, and last terms in the expansion of ( π₯ β 1 ) 6 is 42β337, find all possible real values of π₯ .

Q21:

Find π 6 in the expansion of οΌ 2 4 π₯ + π¦ 4 ο 7 .

Q22:

Find π 6 in the expansion of οΌ 6 π₯ + π¦ 3 ο 8 .

Q23:

Find the second-to-last term in ( 2 + π₯ ) 3 4 .

Q24:

Let π π be the π th term in the expansion of ( π₯ β 2 ) 1 9 in descending powers of π₯ . Find all the nonzero values of π₯ for which 6 π β 5 π + π = 0 8 9 1 0 .

Q25:

Find the general term in οΌ 6 π₯ β 1 6 π₯ ο π + 7 .

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