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In this lesson, we will learn how to expand any binomial expression of the form (a+b)^n.
Q1:
Expand ( 7 + 2 π₯ ) 3 .
Q2:
Find the coefficient of π₯ 1 0 in the expansion of οΉ 1 + π₯ β π₯ ο 2 8 .
Q3:
Consider the expansion of οΉ π₯ + π₯ ο 6 β 6 5 in descending powers of π₯ . What are the possible values of it, if the third term in this expansion is equal to 640?
Q4:
Answer the following questions for the expansion of ( 1 β 3 π₯ ) π .
Given that the coefficient of π₯ 2 is 189, find π .
Hence, work out the value of the coefficient of π₯ 5 .
Q5:
Use the binomial theorem to find the expansion of ( 1 + π₯ ) 4 .
Q6:
Given that and 2 π = 3 π 1 2 , find the values of π and π where π β 0 .
Q7:
Answer the following questions for the expansion of ( 2 + π π₯ ) 6 .
Given that the coefficient of π₯ 2 is 60, and π is positive, find π .
Hence, using your value of π , work out the coefficient of π₯ 5 in the expansion.
Q8:
Find the third term in the expansion of οΌ 1 0 π₯ + 2 3 π₯ ο 2 4 .
Q9:
Find the third term in the expansion of οΌ 3 π₯ + 7 6 π₯ ο 2 4 .
Q10:
Expand οΌ 6 π₯ β 1 3 π₯ ο 2 2 .
Q11:
Expand ( 5 π₯ + 4 π¦ ) 4 .
Q12:
Expand ( π₯ + 2 π¦ ) 2 2 .
Q13:
Expand οΌ π₯ 4 β 1 π₯ ο 5 .
Q14:
Answer the following questions for the expansion of ( 2 + 4 π₯ ) π .
Given that the coefficient of π₯ 2 is 3 8 4 0 , find π .
Q15:
Consider the expansion of Given that the constant of this expansion is 720, find all the possible values of π .
Q16:
Use the binomial theorem to find the expansion of ( π + 2 π ) 4 .
Q17:
Find π₯ given that the ratio of the middle terms in the expansion of ( 1 + π₯ ) 3 is 1 βΆ 2 .
Q18:
Find the two middle terms in the expansion of ( 1 4 π₯ + π¦ ) 3 .
Q19:
Find the coefficient of the fourth term in the expansion of οΌ π₯ + 1 π₯ ο 4 .
Q20:
Which of the following is equal to
Q21:
Q22:
Evaluate ο» β 3 + 1 ο + ο» β 3 β 1 ο 3 3 using the binomial expansion theorem.
Q23:
Use the binomial theorem to expand ( 2 π₯ β 3 π¦ ) 3 .
Q24:
Use the binomial theorem to find the expansion of ( π β π ) 5 .
Q25:
Write the coefficients of the terms that result from the expansion of ( π₯ + π¦ ) 4 .
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