Question 1

Expand the binomial by using Pascal's Triangle to determine the coefficients.​ $( x + 2 y ) ^ { 5 }$ ​

Accepted Answer

A)  $x ^ { 5 } + 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } - 80 x ^ { 2 } y ^ { 3 } + 80 x y ^ { 4 } + 32 y ^ { 5 }$ 
B)  $x ^ { 5 } - 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } + 80 x ^ { 2 } y ^ { 3 } + 80 x y ^ { 4 } + 32 y ^ { 5 }$ 
C)  $x ^ { 5 } + 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } + 80 x ^ { 2 } y ^ { 3 } - 80 x y ^ { 4 } - 32 y ^ { 5 }$ 
D)  $x ^ { 5 } + 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } + 80 x ^ { 2 } y ^ { 3 } + 80 x y ^ { 4 } + 32 y ^ { 5 }$ 
E)  $x ^ { 5 } + 10 x ^ { 4 } y - 40 x ^ { 3 } y ^ { 2 } - 80 x ^ { 2 } y ^ { 3 } - 80 x y ^ { 4 } + 32 y ^ { 5 }$ 
A)  $x ^ { 5 } + 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } - 80 x ^ { 2 } y ^ { 3 } + 80 x y ^ { 4 } + 32 y ^ { 5 }$ 
B)  $x ^ { 5 } - 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } + 80 x ^ { 2 } y ^ { 3 } + 80 x y ^ { 4 } + 32 y ^ { 5 }$ 
C)  $x ^ { 5 } + 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } + 80 x ^ { 2 } y ^ { 3 } - 80 x y ^ { 4 } - 32 y ^ { 5 }$ 
D)  $x ^ { 5 } + 10 x ^ { 4 } y + 40 x ^ { 3 } y ^ { 2 } + 80 x ^ { 2 } y ^ { 3 } + 80 x y ^ { 4 } + 32 y ^ { 5 }$ 
E)  $x ^ { 5 } + 10 x ^ { 4 } y - 40 x ^ { 3 } y ^ { 2 } - 80 x ^ { 2 } y ^ { 3 } - 80 x y ^ { 4 } + 32 y ^ { 5 }$

Question 2

Find the specified nth term in the expansion of the binomial.​ $( x + y ) ^ { 9 } , n = 10$ ​

Accepted Answer

A)  $y ^ { 9 }$ 
B)  $x ^ { 9 } y ^ { 10 }$ 
C)  $x y ^ { 9 }$ 
D)  $x ^ { 9 } y$ 
E)  $y ^ { 10 }$ 
A)  $y ^ { 9 }$ 
B)  $x ^ { 9 } y ^ { 10 }$ 
C)  $x y ^ { 9 }$ 
D)  $x ^ { 9 } y$ 
E)  $y ^ { 10 }$

Question 3

Find the coefficient a of the term in the expansion of the binomial.​ Binomial Terms
$( x - 7 y ) ^ { 10 } ~a x ^ { 8 } y ^ { 2 }$ ​

Accepted Answer

A) 2,208 
B) 2,204 
C) 2,206 
D) 2,205 
E) 2,203 
A) 2,208 
B) 2,204 
C) 2,206 
D) 2,205 
E) 2,203

Question 4

Use the binomial theorem to expand the binomial.​ $( z - y ) ^ { 4 }$ ​

Accepted Answer

A)  $z ^ { 4 } - 4 z ^ { 3 } y + 6 z ^ { 2 } y ^ { 2 } - 4 z y ^ { 3 } + y ^ { 4 }$ 
B)  $z ^ { 4 } - 4 z ^ { 3 } y + 4 z ^ { 2 } y ^ { 2 } - 4 z y ^ { 3 } + y ^ { 4 }$ 
C)  $z ^ { 4 } - 3 z ^ { 3 } y - 3 z y ^ { 3 } + y ^ { 4 }$ 
D)  $z ^ { 4 } - y ^ { 4 }$ 
E)  $z ^ { 4 } + 4 z ^ { 3 } y + 6 z ^ { 2 } y ^ { 2 } + 4 z y ^ { 3 } + y ^ { 4 }$ 
A)  $z ^ { 4 } - 4 z ^ { 3 } y + 6 z ^ { 2 } y ^ { 2 } - 4 z y ^ { 3 } + y ^ { 4 }$ 
B)  $z ^ { 4 } - 4 z ^ { 3 } y + 4 z ^ { 2 } y ^ { 2 } - 4 z y ^ { 3 } + y ^ { 4 }$ 
C)  $z ^ { 4 } - 3 z ^ { 3 } y - 3 z y ^ { 3 } + y ^ { 4 }$ 
D)  $z ^ { 4 } - y ^ { 4 }$ 
E)  $z ^ { 4 } + 4 z ^ { 3 } y + 6 z ^ { 2 } y ^ { 2 } + 4 z y ^ { 3 } + y ^ { 4 }$

Question 5

Find the specified nth term in the expansion of the binomial.(Write the expansion in descending powers of x. ) $( 5 x - 2 y ) ^ { 6 } , n = 3$

Accepted Answer

A)  $20 x ^ { 2 } y ^ { 3 }$ 
B)  $5 x ^ { 2 } y ^ { 4 }$ 
C)  $2500 x ^ { 2 } y ^ { 4 }$ 
D)  $20 x ^ { 2 } y ^ { 4 }$ 
E)  $5 x ^ { 4 } y ^ { 2 }$ 
A)  $20 x ^ { 2 } y ^ { 3 }$ 
B)  $5 x ^ { 2 } y ^ { 4 }$ 
C)  $2500 x ^ { 2 } y ^ { 4 }$ 
D)  $20 x ^ { 2 } y ^ { 4 }$ 
E)  $5 x ^ { 4 } y ^ { 2 }$

Question 6

Find the coefficient a of the term in the expansion of the binomial.​ Binominal Terms
$( x + 7 ) ^ { 12 } a x ^ { 5 }$ ​

Accepted Answer

A) -407,653,785 
B) -652,246,056 
C) 760,953,732 
D) 181,179,460 
E) 652,246,056 
A) -407,653,785 
B) -652,246,056 
C) 760,953,732 
D) 181,179,460 
E) 652,246,056

Question 7

Find the specified nth term in the expansion of the binomial.​ $( x - 10 z ) ^ { 7 } , n = 4$ ​

Accepted Answer

A)  $- 35,000 x ^ { 3 } z ^ { 4 }$ 
B)  $- 35,000 x ^ { 7 } z ^ { 3 }$ 
C)  $- 35,000 x ^ { 4 } z ^ { 3 }$ 
D)  $- 35,000 x ^ { 3 } z ^ { 3 }$ 
E)  $- 35,000 x ^ { 4 } z ^ { 4 }$ 
A)  $- 35,000 x ^ { 3 } z ^ { 4 }$ 
B)  $- 35,000 x ^ { 7 } z ^ { 3 }$ 
C)  $- 35,000 x ^ { 4 } z ^ { 3 }$ 
D)  $- 35,000 x ^ { 3 } z ^ { 3 }$ 
E)  $- 35,000 x ^ { 4 } z ^ { 4 }$

Exam 56: The Binomial Theorem

Expand the binomial by using Pascal's Triangle to determine the coefficients.​ (x+2y)5( x + 2 y ) ^ { 5 }(x+2y)5 ​

Find the specified nth term in the expansion of the binomial.​ (x+y)9,n=10( x + y ) ^ { 9 } , n = 10(x+y)9,n=10 ​

Find the coefficient a of the term in the expansion of the binomial.​ Binomial Terms (x−7y)10 ax8y2( x - 7 y ) ^ { 10 } ~a x ^ { 8 } y ^ { 2 }(x−7y)10 ax8y2 ​

Use the binomial theorem to expand the binomial.​ (z−y)4( z - y ) ^ { 4 }(z−y)4 ​

Find the specified nth term in the expansion of the binomial.(Write the expansion in descending powers of x. ) (5x−2y)6,n=3( 5 x - 2 y ) ^ { 6 } , n = 3(5x−2y)6,n=3

Find the coefficient a of the term in the expansion of the binomial.​ Binominal Terms (x+7)12ax5( x + 7 ) ^ { 12 } a x ^ { 5 }(x+7)12ax5 ​

Find the specified nth term in the expansion of the binomial.​ (x−10z)7,n=4( x - 10 z ) ^ { 7 } , n = 4(x−10z)7,n=4 ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

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Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

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Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

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Multiple Angle and Product to Sum Formulas

Law of Sines

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Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

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Introduction to Conics Parabolas

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Rotation of Conics

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Polar Equations of Conics

Graphs of Polar Equations

Filters

Expand the binomial by using Pascal's Triangle to determine the coefficients. $( x + 2 y ) ^ { 5 }$

Find the specified nth term in the expansion of the binomial. $( x + y ) ^ { 9 } , n = 10$

Find the coefficient a of the term in the expansion of the binomial. Binomial Terms $( x - 7 y ) ^ { 10 } ~a x ^ { 8 } y ^ { 2 }$

Use the binomial theorem to expand the binomial. $( z - y ) ^ { 4 }$

Find the specified nth term in the expansion of the binomial.(Write the expansion in descending powers of x. ) $( 5 x - 2 y ) ^ { 6 } , n = 3$

Find the coefficient a of the term in the expansion of the binomial. Binominal Terms $( x + 7 ) ^ { 12 } a x ^ { 5 }$

Find the specified nth term in the expansion of the binomial. $( x - 10 z ) ^ { 7 } , n = 4$