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In this lesson, we will learn how to find the order and the value of the middle term or terms inside a binomial expansion without the need to fully expand the series.

Q1:

Find the middle term in the expansion of ( 5 π + 7 ) 2 .

Q2:

Find the middle term in the expansion of ( 1 5 π + 3 π ) 2 .

Q3:

For which values of π₯ are the two middle terms of οΎ 1 6 π₯ + π₯ 6 2 5 ο 3 1 9 equal?

Q4:

Given that the middle term in the expansion of ο» π₯ + π π₯ ο 8 is 3 5 8 , find ( 2 π β 2 ) 6 .

Q5:

Consider the expansion of οΌ 2 π₯ + 1 4 π₯ ο 2 2 3 . Are the middle terms of the expansion equal when π₯ = 1 6 ?

Q6:

Given that the middle term in the expansion of ( 6 + π₯ ) 2 4 is equal to 2 Γ π 1 4 , find the value of π₯ .

Q7:

Find the result of dividing the lower-order middle term by the higher one in the expansion of οΌ 6 π₯ + 1 3 π₯ ο 3 5 .

Q8:

In the expansion of ( π π₯ + π ) 2 π + 9 , the two middle terms are equal when π₯ = 9 . Which of the following represents the correct relation between π and π ?

Q9:

Determine the value of π₯ if the value of the middle term in the expansion of οΌ 6 π₯ + 1 1 3 π₯ ο 2 6 is 4β320.

Q10:

Find the middle term in the expansion of οΉ 8 π₯ + 1 3 π₯ ο 4 β 4 4 .

Q11:

Consider the expansion of ( π₯ β π¦ ) ( π β 5 ) . Find the value of π given that the middle terms of the expansion are π 1 0 and π 1 1 .

Q12:

Consider the expansion of ( 5 π₯ β 9 ) 2 π + 1 . Find the value of π₯ given that the middle terms of the expansion are equal.

Q13:

Consider the expansion of οΎ π₯ 9 β 8 6 4 π₯ ο 4 3 5 in descending powers of π₯ . For which values of π₯ is the sum of the two middle terms equal to zero?

Q14:

What is the middle term in the following expansion:

Q15:

Find the two middle terms in the expansion of οΌ 1 4 π₯ + 1 3 π₯ ο 5 3 .

Q16:

Find the two middle terms in the expansion of οΌ 2 π₯ + 1 1 2 π₯ ο 4 2 5 .

Q17:

Given that the two middle terms are equal in the expansion find all possible real values of π₯ .

Q18:

Determine π if π 2 2 is the middle term in the binomial expansion of οΌ π₯ β 1 π₯ ο 2 π + 1 2 .

Q19:

What is the value of π β β€ + that makes the middle term of the binomial expansion of the following independent of π₯ ?

Q20:

Consider the expansion of ( 1 + π₯ ) 6 in ascending powers of π₯ where π₯ β 0 . If the middle term in the expansion is five times the fifth term, what is the value of π₯ ?

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