Math AA SL: Binomial Theorem

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[Maximum Mark: 6]

a) The values in row 3 of Pascal's Triangle are as follows: 1, 3, 3, 1. 
   Write down the values in the next row of Pascal's triangle.

b) Thus, find the term in x^2 of (3x+2)^4.
Detailed Answer/Video Explanations Answer
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[Maximum Mark: 6]

a) Expand (x-3)^{4} and simplify your result

b) Find the x^{2} term in (5x-2)(x-2)^{4}
Detailed Answer/Video Explanations Answer
#MAASL00103

[Maximum Marks: 5]

Consider the binomial expansion of (6x-4)^{10}. 

The term in x^{4} is expressed as _{10}C_a\times(6x)^b\times(-4)^c.

a) Find the values of a, b, and c.

b) Find the coefficient of the term in x^4.
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#MAASL00104

[Maximum Marks: 5]

Consider the binomial expansion of (x+d)^8.

The fourth term of the expansion is 700x^6.

Find the possible values of d.
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#MAASL00106

[Maximum Marks: 7]

Consider the binomial expansion of (4x+1)^n.

The coefficient on the term x^3 is 320n. Thus, find the value of n.
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#MAASL00108

[Maximum Marks: 6]

Consider the expansion of ax^3(3+ax)^9. 

In this expansion, the coefficient of the term containing x^4 is 118098.

Find the value of a.
Detailed Answer/Video Explanations Answer
#MAASL00162

[Maximum Mark: 6]

a) Expand (x-3)^3 and simplify the result.
 
b) Find the term x^2 in (2x+3)(x-3)^3
Detailed Answer/Video Explanations Answer
#MAASL00203

[Maximum Mark: 6]

a) The values in row 5 of Pascal's Triangle are as follows: 1, 5, 10, 10, 5, 1. 
   Write down the values in the next row of Pascal's triangle.

b) Thus, find the term in x^3 of (4x+3)^6.
Detailed Answer/Video Explanations Answer
#MAASL00204

[Maximum Marks: 5]

Consider the binomial expansion of (3x+4)^{7}. 

The term in x^{4} is expressed as _{7}C_a\times(3x)^b\times(4)^c.

a) Find the values of a, b, and c.

b) Find the coefficient of the term in x^4.
Detailed Answer/Video Explanations Answer
#MAASL00205

[Maximum Mark: 6]

a) The values in row 7 of Pascal's Triangle are as follows: 1, 7, 21, 35, 35, 21, 7, 1. 
   Write down the values in the next row of Pascal's triangle.

b) Thus, find the term in x^5 of (2x+6)^8.
Detailed Answer/Video Explanations Answer
#MAASL00206

[Maximum Marks: 7]

Consider the binomial expansion of (2x-7)^{5}. 

The term in x^{2} is expressed as _{5}C_a\times(2x)^b\times(-7)^c.

a) Find the values of a, b, and c.

b) Find the coefficient of the term in x^2.
Detailed Answer/Video Explanations Answer
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[Maximum Marks: 10]

What is the coefficient of x^{4} in the expansion of (2x-1)^{6}(3+3x)^{5}?
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#MAASL00275

[Maximum Marks: 10]

What is the coefficient of x^{2} in the expansion of (4x+3)^{3}(2-3x)^{4}?
Detailed Answer/Video Explanations Answer
#MAASL00276

[Maximum Marks: 7]

Consider the binomial expansion of (2x+7)^n.

The coefficient on the term x^{4} is 11760. Thus, find the value of n.
Detailed Answer/Video Explanations Answer
#MAASL00277

[Maximum Marks: 6]

Expand and simplify (2x+\frac{3}{x})^{3}
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#MAASL00278

[Maximum Marks: 6]

Expand and simplify (x+\frac{4}{x})^{2}
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#MAASL00279

[Maximum Marks: 8]

What is the coefficient of x^{3} in (x-2)^{6}(x+3)^{4}?
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#MAASL00280

[Maximum Marks: 8]

What is the coefficient of x^{2} in (x+2)^{3}(x+5)^{4}?
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#MAASL00281

[Maximum Marks: 4]

Find the value of x if _{x}C_{6}=84
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#MAASL00282

[Maximum Marks: 4]

Find the value of x if _{x}C_{7}=792
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