Question 1

Expand the binomial by using Pascal's triangle to determine the coefficients.
$$( 5 x - 4 y ) ^ { 6 }$$

Accepted Answer

A)  $15625 x ^ { 6 } - 75000 x ^ { 5 } y + 150000 x ^ { 4 } y ^ { 2 } - 160000 x ^ { 3 } y ^ { 3 } + 150000 x ^ { 2 } y ^ { 4 } - 30720 x y ^ { 5 } + 4096 y ^ { 6 }$ 
B)  $15625 x ^ { 6 } - 75000 x ^ { 5 } y + 100000 x ^ { 4 } y ^ { 2 } - 160000 x ^ { 3 } y ^ { 3 } + 96000 x ^ { 2 } y ^ { 4 } - 30720 x y ^ { 5 } + 4096 y ^ { 6 }$ 
C)  $15625 x ^ { 6 } - 75000 x ^ { 5 } y + 150000 x ^ { 4 } y ^ { 2 } - 160000 x ^ { 3 } y ^ { 3 } + 128000 x ^ { 2 } y ^ { 4 } - 30720 x y ^ { 5 } + 4096 y ^ { 6 }$ 
D)  $15625 x ^ { 6 } - 75000 x ^ { 5 } y + 150000 x ^ { 4 } y ^ { 2 } - 160000 x ^ { 3 } y ^ { 3 } + 96000 x ^ { 2 } y ^ { 4 } - 30720 x y ^ { 5 } + 4096 y ^ { 6 }$ 
E)  $\quad 15625 x ^ { 6 } - 75000 x ^ { 5 } y + 96000 x ^ { 4 } y ^ { 2 } - 160000 x ^ { 3 } y ^ { 3 } + 96000 x ^ { 2 } y ^ { 4 } - 30720 x y ^ { 5 } + 4096 y ^ { 6 }$ 
A)  $15625 x ^ { 6 } - 75000 x ^ { 5 } y + 150000 x ^ { 4 } y ^ { 2 } - 160000 x ^ { 3 } y ^ { 3 } + 150000 x ^ { 2 } y ^ { 4 } - 30720 x y ^ { 5 } + 4096 y ^ { 6 }$ 
B)  $15625 x ^ { 6 } - 75000 x ^ { 5 } y + 100000 x ^ { 4 } y ^ { 2 } - 160000 x ^ { 3 } y ^ { 3 } + 96000 x ^ { 2 } y ^ { 4 } - 30720 x y ^ { 5 } + 4096 y ^ { 6 }$ 
C)  $15625 x ^ { 6 } - 75000 x ^ { 5 } y + 150000 x ^ { 4 } y ^ { 2 } - 160000 x ^ { 3 } y ^ { 3 } + 128000 x ^ { 2 } y ^ { 4 } - 30720 x y ^ { 5 } + 4096 y ^ { 6 }$ 
D)  $15625 x ^ { 6 } - 75000 x ^ { 5 } y + 150000 x ^ { 4 } y ^ { 2 } - 160000 x ^ { 3 } y ^ { 3 } + 96000 x ^ { 2 } y ^ { 4 } - 30720 x y ^ { 5 } + 4096 y ^ { 6 }$ 
E)  $\quad 15625 x ^ { 6 } - 75000 x ^ { 5 } y + 96000 x ^ { 4 } y ^ { 2 } - 160000 x ^ { 3 } y ^ { 3 } + 96000 x ^ { 2 } y ^ { 4 } - 30720 x y ^ { 5 } + 4096 y ^ { 6 }$

Question 2

Use mathematical induction to prove the following for every positive integer $n$.
$$\sum _ { i = 1 } ^ { n } \frac { 5 } { ( 2 i - 1 ) ( 2 i + 1 ) } = \frac { 5 n } { 2 n + 1 }$$

Accepted Answer

i. Show true for @#LAT-DLM&
\[\begin{aligned}
\fra

Question 3

Use mathematical induction to prove that 80 is a factor of $2 ^ { 8 n + 2 } + 16$ 6 for all positive n.

Accepted Answer

None

Question 4

Find a formula for the nth term of the following geometric sequence, then find the 4th term of the sequence. $9,36,144 , \ldots$

Accepted Answer

A)  $a _ { n } = 9 ( 4 ) ^ { n } ; a _ { 4 } = 576$ 
B)  $a _ { n } = 9 ( 4 ) ^ { n } ; a _ { 4 } = 2304$ 
C)  $a _ { n } = 9 ( 4 ) ^ { n - 1 } ; a _ { 4 } = 2304$ 
D)  $a _ { n } = 9 ( 4 ) ^ { n - 1 } ; a _ { 4 } = 576$ 
E)  $a _ { n } = 9 ( 4 ) ^ { n - 1 } ; a _ { 4 } = 144$ 
A)  $a _ { n } = 9 ( 4 ) ^ { n } ; a _ { 4 } = 576$ 
B)  $a _ { n } = 9 ( 4 ) ^ { n } ; a _ { 4 } = 2304$ 
C)  $a _ { n } = 9 ( 4 ) ^ { n - 1 } ; a _ { 4 } = 2304$ 
D)  $a _ { n } = 9 ( 4 ) ^ { n - 1 } ; a _ { 4 } = 576$ 
E)  $a _ { n } = 9 ( 4 ) ^ { n - 1 } ; a _ { 4 } = 144$

Question 5

Find the sum of the finite geometric sequence.
$$\sum _ { n = 1 } ^ { 5 } - \left( - \frac { 1 } { 6 } \right) ^ { n - 1 }$$

Accepted Answer

A)  $\frac { 6665 } { 1296 }$ 
B)  $- \frac { 1 } { 6 }$ 
C)  1111 
D)  $\frac { 185 } { 216 }$ 
E)  $- \frac { 1111 } { 1296 }$ 
A)  $\frac { 6665 } { 1296 }$ 
B)  $- \frac { 1 } { 6 }$ 
C)  1111 
D)  $\frac { 185 } { 216 }$ 
E)  $- \frac { 1111 } { 1296 }$

Question 6

Use mathematical induction to prove the following for every positive integer $n$.
$$1 + 6 + 36 + 216 + \ldots + 6 ^ { n - 1 } = \frac { 6 ^ { n } - 1 } { 5 }$$

Accepted Answer

i. Show true for @#LAT-DLM&
\[\begin{aligned}
6 ^

Question 7

Use mathematical induction to prove the following for every positive integer n. $$\sum _ { i = 1 } ^ { n } \frac { 17 } { i ( i + 1 ) ( i + 2 ) } = \frac { 17 n ( n + 3 ) } { 4 ( n + 1 ) ( n + 2 ) }$$

Accepted Answer

i. Show true for @#LAT-DLM&
\[\begin{aligned}
\fra

Question 8

Use mathematical induction to prove the formula for every positive integer $n$. Show all your work.
$$7 + 10 + 13 + 16 + \ldots + ( 3 n + 4 ) = \frac { n } { 2 } ( 3 n + 11 )$$

Accepted Answer

1) When @#LAT-DLM&. The formula is valid for @#LAT-DLM&.
2)

Question 9

Determine whether the sequence is geometric. If so, find the common ratio.
$- 1 , - 2 , - 4 , - 8 , \ldots$

Accepted Answer

A)  2 
B) - 1 
C)  $\frac { 1 } { 2 }$ 
D)  - 2 
E)  not geometric 
A)  2 
B) - 1 
C)  $\frac { 1 } { 2 }$ 
D)  - 2 
E)  not geometric

Question 10

Find the indicated $n$th term of the geometric sequence.
6th term: $a _ { 5 } = \frac { 4 } { 81 } , a _ { 8 } = \frac { 4 } { 2187 }$

Accepted Answer

A)  $\frac { 4 } { 729 }$ 
B)  $\frac { 3 } { 1024 }$ 
C)  $\frac { 4 } { 2187 }$ 
D)  $\frac { 4 } { 243 }$ 
E)  $\frac { 4 } { 81 }$ 
A)  $\frac { 4 } { 729 }$ 
B)  $\frac { 3 } { 1024 }$ 
C)  $\frac { 4 } { 2187 }$ 
D)  $\frac { 4 } { 243 }$ 
E)  $\frac { 4 } { 81 }$

Question 11

Use the Binomial Theorem to expand the complex number. Simplify your result. $( - 2 + 5 i ) ^ { 4 }$

Accepted Answer

A)  $41 + 840 i$ 
B)  $41 - 840 i$ 
C)  $- 41 + 840 i$ 
D)  $- 41 - 840 i$ 
E)  16 
A)  $41 + 840 i$ 
B)  $41 - 840 i$ 
C)  $- 41 + 840 i$ 
D)  $- 41 - 840 i$ 
E)  16

Question 12

Determine whether the sequence is geometric. If so, find the common ratio.
$- 1,3,7,11 , \ldots$

Accepted Answer

A)  4 
B)  $- 1$ 
C)  $\frac { 1 } { 4 }$ 
D)  $- 4$ 
E)  not geometric 
A)  4 
B)  $- 1$ 
C)  $\frac { 1 } { 4 }$ 
D)  $- 4$ 
E)  not geometric

Question 13

Find the sum of the following infinite geometric series.
$$- 14 + 13 - \frac { 169 } { 14 } + \frac { 2197 } { 196 } - \ldots$$

Accepted Answer

A)  $- \frac { 27 } { 196 }$ 
B)  $- \frac { 1 } { 196 }$ 
C)  $\frac { 27 } { 196 }$ 
D)  $- 14$ 
E)  $- \frac { 196 } { 27 }$ 
A)  $- \frac { 27 } { 196 }$ 
B)  $- \frac { 1 } { 196 }$ 
C)  $\frac { 27 } { 196 }$ 
D)  $- 14$ 
E)  $- \frac { 196 } { 27 }$

Question 14

Find a formula for $a _ { n }$ for the arithmetic sequence.
$$a _ { 4 } = 10 , a _ { 8 } = 34$$

Accepted Answer

A)  $a _ { n } = - 8 + 6 n$ 
B)  $a _ { n } = 14 - 8 n$ 
C)  $a _ { n } = 6 - 8 n$ 
D)  $a _ { n } = - 8 ( 6 ) ^ { n }$ 
E)  $a _ { n } = - 14 + 6 n$ 
A)  $a _ { n } = - 8 + 6 n$ 
B)  $a _ { n } = 14 - 8 n$ 
C)  $a _ { n } = 6 - 8 n$ 
D)  $a _ { n } = - 8 ( 6 ) ^ { n }$ 
E)  $a _ { n } = - 14 + 6 n$

Question 15

Use mathematical induction to prove the following for every positive integer $n$.
$$\sum _ { i = 1 } ^ { n } \frac { 15 } { ( 2 i - 1 ) ( 2 i + 1 ) } = \frac { 15 n } { 2 n + 1 }$$

Accepted Answer

i. Show true for @#LAT-DLM&
\[\begin{aligned}
\fra

Question 16

Find the indicated sum.
$$\sum _ { n = 1 } ^ { 8 } n ^ { 4 }$$

Accepted Answer

A)  4096 
B)  1,679,616 
C)  36 
D)  87,380 
E)  8772 
A)  4096 
B)  1,679,616 
C)  36 
D)  87,380 
E)  8772

Question 17

Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that $n$ begins with 1.)
$$a _ { n } = - 6 + 4 n$$

Accepted Answer

A)  $- 4$ 
B)  6 
C)  $- 6$ 
D)  4 
E)  not arithmetic 
A)  $- 4$ 
B)  6 
C)  $- 6$ 
D)  4 
E)  not arithmetic

Question 18

Find the probability for the experiment of tossing a coin four times and getting at least two heads. Use the sample space
$S=\begin{array}{cccc}
H H H H & H H H T & H H T H & H T H H \
\text { THHH } & H H T T & H T H T & T H H T \
T H T H & H T T H & T T H H & T T H \
\text { TTHT } & \text { THTT } & H T T T & T T T T
\end{array}$

Accepted Answer

A)  $\frac { 11 } { 16 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 13 } { 16 }$ 
D)  $\frac { 7 } { 8 }$ 
E)  $\frac { 5 } { 8 }$ 
A)  $\frac { 11 } { 16 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 13 } { 16 }$ 
D)  $\frac { 7 } { 8 }$ 
E)  $\frac { 5 } { 8 }$

Question 19

Use the Binomial Theorem to expand and simplify the expression.
$$\left( x ^ { 3 / 4 } - 5 \right) ^ { 4 }$$

Accepted Answer

A)  $x ^ { 3 } + 625$ 
B)  $x ^ { 12 } - 20 x ^ { 9 } + 150 x ^ { 6 } - 500 x ^ { 3 } + 625$ 
C)  $x ^ { 3 } - 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } - 500 x ^ { 3 / 4 } + 625$ 
D)  $x ^ { 3 } + 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } + 500 x ^ { 3 / 4 } + 625$ 
E)  $x ^ { 12 } + 20 x ^ { 9 } + 150 x ^ { 6 } + 500 x ^ { 3 } + 625$ 
A)  $x ^ { 3 } + 625$ 
B)  $x ^ { 12 } - 20 x ^ { 9 } + 150 x ^ { 6 } - 500 x ^ { 3 } + 625$ 
C)  $x ^ { 3 } - 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } - 500 x ^ { 3 / 4 } + 625$ 
D)  $x ^ { 3 } + 20 x ^ { 9 / 4 } + 150 x ^ { 3 / 2 } + 500 x ^ { 3 / 4 } + 625$ 
E)  $x ^ { 12 } + 20 x ^ { 9 } + 150 x ^ { 6 } + 500 x ^ { 3 } + 625$

Expand the binomial by using Pascal's triangle to determine the coefficients. $( 5 x - 4 y ) ^ { 6 }$

Use mathematical induction to prove the following for every positive integer $n$ . $\sum _ { i = 1 } ^ { n } \frac { 5 } { ( 2 i - 1 ) ( 2 i + 1 ) } = \frac { 5 n } { 2 n + 1 }$

Use mathematical induction to prove that 80 is a factor of $2 ^ { 8 n + 2 } + 16$ 6 for all positive n.

Find a formula for the nth term of the following geometric sequence, then find the 4th term of the sequence. $9,36,144 , \ldots$

Find the sum of the finite geometric sequence. $\sum _ { n = 1 } ^ { 5 } - \left( - \frac { 1 } { 6 } \right) ^ { n - 1 }$

Use mathematical induction to prove the following for every positive integer $n$ . $1 + 6 + 36 + 216 + \ldots + 6 ^ { n - 1 } = \frac { 6 ^ { n } - 1 } { 5 }$

Use mathematical induction to prove the following for every positive integer n. $\sum _ { i = 1 } ^ { n } \frac { 17 } { i ( i + 1 ) ( i + 2 ) } = \frac { 17 n ( n + 3 ) } { 4 ( n + 1 ) ( n + 2 ) }$

Use mathematical induction to prove the formula for every positive integer $n$ . Show all your work. $7 + 10 + 13 + 16 + \ldots + ( 3 n + 4 ) = \frac { n } { 2 } ( 3 n + 11 )$

Determine whether the sequence is geometric. If so, find the common ratio. $- 1 , - 2 , - 4 , - 8 , \ldots$

Find the indicated $n$ th term of the geometric sequence. 6th term: $a _ { 5 } = \frac { 4 } { 81 } , a _ { 8 } = \frac { 4 } { 2187 }$

Use the Binomial Theorem to expand the complex number. Simplify your result. $( - 2 + 5 i ) ^ { 4 }$

Determine whether the sequence is geometric. If so, find the common ratio. $- 1,3,7,11 , \ldots$

Find the sum of the following infinite geometric series. $- 14 + 13 - \frac { 169 } { 14 } + \frac { 2197 } { 196 } - \ldots$

Find a formula for $a _ { n }$ for the arithmetic sequence. $a _ { 4 } = 10 , a _ { 8 } = 34$

Use mathematical induction to prove the following for every positive integer $n$ . $\sum _ { i = 1 } ^ { n } \frac { 15 } { ( 2 i - 1 ) ( 2 i + 1 ) } = \frac { 15 n } { 2 n + 1 }$

Find the indicated sum. $\sum _ { n = 1 } ^ { 8 } n ^ { 4 }$

Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that $n$ begins with 1.) $a _ { n } = - 6 + 4 n$

Find the probability for the experiment of tossing a coin four times and getting at least two heads. Use the sample space Sequals HHHH HHHT HHTH HTHH THHH HHTT HTHT THHT THTH HTTH TTHH TTH TTHT THTT HTTT TTTT

Use the Binomial Theorem to expand and simplify the expression. $\left( x ^ { 3 / 4 } - 5 \right) ^ { 4 }$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Exam 8: Sequences, Series, and Probability

Expand the binomial by using Pascal's triangle to determine the coefficients. (5x−4y)6( 5 x - 4 y ) ^ { 6 }(5x−4y)6

Use mathematical induction to prove the following for every positive integer nnn . ∑i=1n5(2i−1)(2i+1)=5n2n+1\sum _ { i = 1 } ^ { n } \frac { 5 } { ( 2 i - 1 ) ( 2 i + 1 ) } = \frac { 5 n } { 2 n + 1 }∑i=1n​(2i−1)(2i+1)5​=2n+15n​

Use mathematical induction to prove that 80 is a factor of 28n+2+162 ^ { 8 n + 2 } + 1628n+2+16 6 for all positive n.

Find a formula for the nth term of the following geometric sequence, then find the 4th term of the sequence. 9,36,144,…9,36,144 , \ldots9,36,144,…

Find the sum of the finite geometric sequence. ∑n=15−(−16)n−1\sum _ { n = 1 } ^ { 5 } - \left( - \frac { 1 } { 6 } \right) ^ { n - 1 }∑n=15​−(−61​)n−1

Use mathematical induction to prove the following for every positive integer nnn . 1+6+36+216+…+6n−1=6n−151 + 6 + 36 + 216 + \ldots + 6 ^ { n - 1 } = \frac { 6 ^ { n } - 1 } { 5 }1+6+36+216+…+6n−1=56n−1​

Use mathematical induction to prove the following for every positive integer n. ∑i=1n17i(i+1)(i+2)=17n(n+3)4(n+1)(n+2)\sum _ { i = 1 } ^ { n } \frac { 17 } { i ( i + 1 ) ( i + 2 ) } = \frac { 17 n ( n + 3 ) } { 4 ( n + 1 ) ( n + 2 ) }∑i=1n​i(i+1)(i+2)17​=4(n+1)(n+2)17n(n+3)​

Use mathematical induction to prove the formula for every positive integer nnn . Show all your work. 7+10+13+16+…+(3n+4)=n2(3n+11)7 + 10 + 13 + 16 + \ldots + ( 3 n + 4 ) = \frac { n } { 2 } ( 3 n + 11 )7+10+13+16+…+(3n+4)=2n​(3n+11)

Determine whether the sequence is geometric. If so, find the common ratio. −1,−2,−4,−8,…- 1 , - 2 , - 4 , - 8 , \ldots−1,−2,−4,−8,…

Find the indicated nnn th term of the geometric sequence. 6th term: a5=481,a8=42187a _ { 5 } = \frac { 4 } { 81 } , a _ { 8 } = \frac { 4 } { 2187 }a5​=814​,a8​=21874​

Use the Binomial Theorem to expand the complex number. Simplify your result. (−2+5i)4( - 2 + 5 i ) ^ { 4 }(−2+5i)4

Determine whether the sequence is geometric. If so, find the common ratio. −1,3,7,11,…- 1,3,7,11 , \ldots−1,3,7,11,…

Find the sum of the following infinite geometric series. −14+13−16914+2197196−…- 14 + 13 - \frac { 169 } { 14 } + \frac { 2197 } { 196 } - \ldots−14+13−14169​+1962197​−…

Find a formula for ana _ { n }an​ for the arithmetic sequence. a4=10,a8=34a _ { 4 } = 10 , a _ { 8 } = 34a4​=10,a8​=34

Use mathematical induction to prove the following for every positive integer nnn . ∑i=1n15(2i−1)(2i+1)=15n2n+1\sum _ { i = 1 } ^ { n } \frac { 15 } { ( 2 i - 1 ) ( 2 i + 1 ) } = \frac { 15 n } { 2 n + 1 }∑i=1n​(2i−1)(2i+1)15​=2n+115n​

Find the indicated sum. ∑n=18n4\sum _ { n = 1 } ^ { 8 } n ^ { 4 }∑n=18​n4

Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that nnn begins with 1.) an=−6+4na _ { n } = - 6 + 4 nan​=−6+4n

Find the probability for the experiment of tossing a coin four times and getting at least two heads. Use the sample space Sequals HHHH HHHT HHTH HTHH THHH HHTT HTHT THHT THTH HTTH TTHH TTH TTHT THTT HTTT TTTT

Use the Binomial Theorem to expand and simplify the expression. (x3/4−5)4\left( x ^ { 3 / 4 } - 5 \right) ^ { 4 }(x3/4−5)4

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Expand the binomial by using Pascal's triangle to determine the coefficients. $( 5 x - 4 y ) ^ { 6 }$

Use mathematical induction to prove the following for every positive integer $n$ . $\sum _ { i = 1 } ^ { n } \frac { 5 } { ( 2 i - 1 ) ( 2 i + 1 ) } = \frac { 5 n } { 2 n + 1 }$

Use mathematical induction to prove that 80 is a factor of $2 ^ { 8 n + 2 } + 16$ 6 for all positive n.

Find a formula for the nth term of the following geometric sequence, then find the 4th term of the sequence. $9,36,144 , \ldots$

Find the sum of the finite geometric sequence. $\sum _ { n = 1 } ^ { 5 } - \left( - \frac { 1 } { 6 } \right) ^ { n - 1 }$

Use mathematical induction to prove the following for every positive integer $n$ . $1 + 6 + 36 + 216 + \ldots + 6 ^ { n - 1 } = \frac { 6 ^ { n } - 1 } { 5 }$

Use mathematical induction to prove the following for every positive integer n. $\sum _ { i = 1 } ^ { n } \frac { 17 } { i ( i + 1 ) ( i + 2 ) } = \frac { 17 n ( n + 3 ) } { 4 ( n + 1 ) ( n + 2 ) }$

Use mathematical induction to prove the formula for every positive integer $n$ . Show all your work. $7 + 10 + 13 + 16 + \ldots + ( 3 n + 4 ) = \frac { n } { 2 } ( 3 n + 11 )$

Determine whether the sequence is geometric. If so, find the common ratio. $- 1 , - 2 , - 4 , - 8 , \ldots$

Find the indicated $n$ th term of the geometric sequence. 6th term: $a _ { 5 } = \frac { 4 } { 81 } , a _ { 8 } = \frac { 4 } { 2187 }$

Use the Binomial Theorem to expand the complex number. Simplify your result. $( - 2 + 5 i ) ^ { 4 }$

Determine whether the sequence is geometric. If so, find the common ratio. $- 1,3,7,11 , \ldots$

Find the sum of the following infinite geometric series. $- 14 + 13 - \frac { 169 } { 14 } + \frac { 2197 } { 196 } - \ldots$

Find a formula for $a _ { n }$ for the arithmetic sequence. $a _ { 4 } = 10 , a _ { 8 } = 34$

Use mathematical induction to prove the following for every positive integer $n$ . $\sum _ { i = 1 } ^ { n } \frac { 15 } { ( 2 i - 1 ) ( 2 i + 1 ) } = \frac { 15 n } { 2 n + 1 }$

Find the indicated sum. $\sum _ { n = 1 } ^ { 8 } n ^ { 4 }$

Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that $n$ begins with 1.) $a _ { n } = - 6 + 4 n$

Use the Binomial Theorem to expand and simplify the expression. $\left( x ^ { 3 / 4 } - 5 \right) ^ { 4 }$