Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to find the coefficient of a term in a binomial expansion using the general rule without the need to fully expand the series.

Q1:

Determine the coefficient of ๐ 2 in the expansion of ๏ผ ๐ 1 1 + 1 1 6 ๐ ๏ 1 2 .

Q2:

Answer the following questions for the expansion of ( 1 + ๐ ๐ฅ ) 5 .

Given that the coefficient of ๐ฅ 2 is 160, and ๐ is positive, find ๐ .

Hence, using your value of ๐ , work out the first three terms in ascending powers of ๐ฅ in the expansion.

Q3:

Find the coefficient of ๐ ๏ญ ๏ in the expansion of ๏ผ ๐ โ 1 2 ๐ ๏ ๏ฎ ๏จ ๏ , where ๐ โ ๐ ๏ฐ .

Q4:

In the expansion of a binomial, determine which of the following is equivalent to the relation 2 ( ๐ ) = ๐ + ๐ c o e ๏ฌ c i e n t o f c o e ๏ฌ c i e n t o f c o e ๏ฌ c i e n t o f 1 0 9 1 1 .

Q5:

Consider the expansion of ๏ผ ๐ฅ 4 + 2 ๐ฅ ๏ 4 1 7 . Is the coefficient of ๐ฅ 2 nonzero?

Q6:

Find the coefficient of ๐ฅ 8 in the expansion of ๏ ( 3 + ๐ฅ ) + 9 ( 3 + ๐ฅ ) ( 6 + ๐ฅ ) + 3 6 ( 3 + ๐ฅ ) ( 6 + ๐ฅ ) + โฏ + ( 6 + ๐ฅ ) ๏ 9 8 7 2 9 .

Q7:

In the expansion of ( 1 + ๐ฅ ) 3 ๐ in ascending powers of ๐ฅ , ๐ ๐ denotes the ๐ th term.

If, in the expansion of ( 1 + ๐ฅ ) 3 ๐ , the coefficients of ๐ ๐ + 2 and ๐ 2 ๐ โ 5 are equal, which of the following describes the possible values of ๐ ?

Q8:

Find the coefficient of ๐ฅ 7 in the expansion of ๏ผ 2 + 3 ๐ฅ 5 ๏ 1 1 .

Q9:

In an expansion, if 2 ( coefficient of ๐ ) = 2 8 coefficient of ๐ + 2 7 coefficient of ๐ 2 9 , find ๐ .

Q10:

Consider the expansion of ( 1 + ๐ฅ ) 2 3 . Find all possible values of ๐ such that the coefficients of ๐ 2 ๐ + 7 and ๐ ๐ + 9 are equal.

Q11:

Find the coefficient of ๐ฅ 5 in the expansion of ( 2 โ 5 ๐ฅ ) 8 .

Q12:

If the order of the term free of ๐ฅ in ๏ผ 2 ๐ฅ โ 8 ๐ฅ ๏ 2 1 8 is equal to the term free of ๐ฅ in ๏ผ ๐ฅ โ 2 ๐ฅ ๏ 6 2 ๐ , find ๐ .

Q13:

Find the coefficient of the ๐ t h term in the expansion of ๏ฟ ๐ฅ โ 1 1 โ 1 ๐ฅ โ 1 1 ๏ 7 4 2 ๐ .

Q14:

Use Pascalโs triangle to determine the coefficients of the terms that result from the expansion of ( ๐ฅ + ๐ฆ ) 6 .

Q15:

Determine the coefficient of ๐ฅ โ 6 in the expansion of ๏ผ ๐ฅ + 1 ๐ฅ ๏ 2 6 .

Q16:

Determine the coefficient of ๐ฅ โ 1 in the expansion of ๏ผ ๐ฅ + 1 ๐ฅ ๏ 4 4 .

Q17:

Consider the expansion of ( ๐ ๐ฅ + ๐ ) 4 in descending powers of ๐ฅ . Given that the coefficient of the third term is 2 7 9 8 , find all possible values of ๐ ๐ .

Q18:

Find the coefficient of ๐ฅ 5 in the expansion of ๏น 1 + ๐ฅ โ ๐ฅ ๏ ( 1 + ๐ฅ ) 2 1 8 .

Q19:

Find the coefficient of ๏ฝ ๐ฅ ๐ฆ ๏ 6 in the expansion of ๏ฝ 2 ๐ฅ ๐ฆ + ๐ฆ 2 ๐ฅ ๏ 1 0 .

Q20:

In the expansion of ๏ผ ๐ฅ + 1 ๐ ๐ฅ ๏ 2 4 , if the coefficient of the middle term equals the coefficient of ๐ฅ 5 , find the value of ๐ .

Q21:

Find the coefficient of ๐ 1 2 in 2 4 ๐ ๏พ ๐ 4 + 4 ๐ ๏ 8 2 3 1 7 .

Q22:

Find the coefficient of ๐ฅ 8 in the expansion of ๏ผ ๐ฅ + 2 ๐ฅ ๏ ๏ผ ๐ฅ โ 2 ๐ฅ ๏ 1 0 1 0 .

Q23:

Find the coefficient of ๐ฅ 2 in ( 1 โ ๐ฅ ) ( 5 โ 2 ๐ฅ ) 6 3 .

Q24:

Find the coefficient of ๐ฅ 3 in the expansion of ( 2 + 3 ๐ฅ ) 8 .

Q25:

The coefficient of ๐ฅ 2 in the expansion of ( 1 + 2 ๐ฅ ) ๐ is 144. Find the value of ๐ .

Donโt have an account? Sign Up