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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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