Question 1

Calculate the binomial coefficient.​ ${ } _ { 29 } C _ { 29 }$ ​

Accepted Answer

A) 0 
B) 4 
C) 1 
D) 3 
E) 2 
A) 0 
B) 4 
C) 1 
D) 3 
E) 2

Question 2

Use the binomial theorem to expand the binomial.​ $( a + b ) ^ { 4 }$

Accepted Answer

The answer of Use the binomial theorem to expand the...

Question 3

Calculate the binomial coefficient: ${ } _ { 11 } C _ { 8 }$

Accepted Answer

A) 6652800 
B) 88 
C) 165 
D) 1 
E) 0 
A) 6652800 
B) 88 
C) 165 
D) 1 
E) 0

Question 4

Use the Binomial Theorem to expand and simplify the expression.​ $2 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }$ ​

Accepted Answer

A)  $2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375$ 
B)  $2 x ^ { 4 } + 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375$ 
C)  $2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x + 1375$ 
D)  $2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x - 1375$ 
E)  $2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x - 1375$ 
A)  $2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375$ 
B)  $2 x ^ { 4 } + 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375$ 
C)  $2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x + 1375$ 
D)  $2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x - 1375$ 
E)  $2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x - 1375$

Question 5

Use the Binomial Theorem to expand and simplify the expression.​ $( y - 3 ) ^ { 5 }$ ​

Accepted Answer

A)  $y ^ { 5 } - 15 y ^ { 4 } + 90 y ^ { 3 } - 270 y ^ { 2 } + 405 y - 243$ 
B)  $y ^ { 5 } - 15 y ^ { 4 } - 90 y ^ { 3 } - 270 y ^ { 2 } + 405 y - 243$ 
C)  $y ^ { 5 } + 15 y ^ { 4 } - 90 y ^ { 3 } + 270 y ^ { 2 } - 405 y + 243$ 
D)  $y ^ { 5 } - 15 y ^ { 4 } + 90 y ^ { 3 } - 270 y ^ { 2 } - 405 y - 243$ 
E)  $y ^ { 5 } - 15 y ^ { 4 } - 90 y ^ { 3 } - 270 y ^ { 2 } - 405 y - 243$ 
A)  $y ^ { 5 } - 15 y ^ { 4 } + 90 y ^ { 3 } - 270 y ^ { 2 } + 405 y - 243$ 
B)  $y ^ { 5 } - 15 y ^ { 4 } - 90 y ^ { 3 } - 270 y ^ { 2 } + 405 y - 243$ 
C)  $y ^ { 5 } + 15 y ^ { 4 } - 90 y ^ { 3 } + 270 y ^ { 2 } - 405 y + 243$ 
D)  $y ^ { 5 } - 15 y ^ { 4 } + 90 y ^ { 3 } - 270 y ^ { 2 } - 405 y - 243$ 
E)  $y ^ { 5 } - 15 y ^ { 4 } - 90 y ^ { 3 } - 270 y ^ { 2 } - 405 y - 243$

Question 6

Use the Binomial Theorem to expand and simplify the expression.​ $( 2 \sqrt { t } - 5 ) ^ { 3 }$ ​

Accepted Answer

A)  $8 t ^ { 3 / 2 } - 60 t + 150 t ^ { 1 / 2 } - 125$ 
B)  $8 t ^ { 3 / 2 } - 60 t + 150 t ^ { 1 / 2 } + 125$ 
C)  $8 t ^ { 3 / 2 } - 60 t - 150 t ^ { 1 / 2 } - 125$ 
D)  $8 t ^ { 3 / 2 } + 60 t + 150 t ^ { 1 / 2 } + 125$ 
E)  $8 t ^ { 3 / 2 } + 60 t - 150 t ^ { 1 / 2 } - 125$ 
A)  $8 t ^ { 3 / 2 } - 60 t + 150 t ^ { 1 / 2 } - 125$ 
B)  $8 t ^ { 3 / 2 } - 60 t + 150 t ^ { 1 / 2 } + 125$ 
C)  $8 t ^ { 3 / 2 } - 60 t - 150 t ^ { 1 / 2 } - 125$ 
D)  $8 t ^ { 3 / 2 } + 60 t + 150 t ^ { 1 / 2 } + 125$ 
E)  $8 t ^ { 3 / 2 } + 60 t - 150 t ^ { 1 / 2 } - 125$

Question 7

Find the specified nth term in the expansion of the binomial.​ $( 5 x - 3 y ) ^ { 12 } , n = 10$ ​

Accepted Answer

A)  $- 541,282,500 y x$ 
B)  $- 541,282,500 y ^ { 3 } x ^ { 3 }$ 
C)  $- 541,282,500 y ^ { 9 } x ^ { 3 }$ 
D)  $- 541,282,500 y ^ { 9 } x ^ { 9 }$ 
E)  $- 541,282,500 y ^ { 3 } x ^ { 9 }$ 
A)  $- 541,282,500 y x$ 
B)  $- 541,282,500 y ^ { 3 } x ^ { 3 }$ 
C)  $- 541,282,500 y ^ { 9 } x ^ { 3 }$ 
D)  $- 541,282,500 y ^ { 9 } x ^ { 9 }$ 
E)  $- 541,282,500 y ^ { 3 } x ^ { 9 }$

Question 8

The probability that a basketball player will make a given free throw is $\frac { 6 } { 10 }$ .To find the probability that the player makes exactly 8 out of her next 10 free throws,evaluate the term ${ } _ { 10 } C _ { 8 } \left( \frac { 6 } { 10 } \right) ^ { 8 } \left( \frac { 4 } { 10 } \right) ^ { 2 }$ in the expansion of $\left( \frac { 6 } { 10 } + \frac { 4 } { 10 } \right) ^ { 10 }$ .Round to four decimal places.

Accepted Answer

A) 0.2721 
B) 0.0106 
C) 0.0047 
D) 0.7558 
E) 0.1209 
A) 0.2721 
B) 0.0106 
C) 0.0047 
D) 0.7558 
E) 0.1209

Question 9

Use the Binomial Theorem to expand and simplify the expression. $( 4 x + 5 y ) ^ { 4 }$

Accepted Answer

A)  $256 x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + 625 y ^ { 4 }$ 
B)  $256 x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } - y ^ { 4 }$ 
C)  $256 x ^ { 4 } + 320 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + 625 y ^ { 4 }$ 
D)  $256 x ^ { 4 } + 500 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } - 625 y ^ { 4 }$ 
E)  $x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + y ^ { 4 }$ 
A)  $256 x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + 625 y ^ { 4 }$ 
B)  $256 x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } - y ^ { 4 }$ 
C)  $256 x ^ { 4 } + 320 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + 625 y ^ { 4 }$ 
D)  $256 x ^ { 4 } + 500 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } - 625 y ^ { 4 }$ 
E)  $x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + y ^ { 4 }$

Question 10

Find the specified nth term in the expansion of the binomial.​ $( 4 x + 3 y ) ^ { 9 } , n = 8$ ​

Accepted Answer

A)  $1,259,712 x ^ { 7 } y ^ { 2 }$ 
B)  $1,259,712 x ^ { 2 } y ^ { 7 }$ 
C)  $1,259,712 x ^ { 8 } y ^ { 9 }$ 
D)  $1,259,712 x ^ { 2 } y ^ { 2 }$ 
E)  $1,259,712 x ^ { 7 } y ^ { 7 }$ 
A)  $1,259,712 x ^ { 7 } y ^ { 2 }$ 
B)  $1,259,712 x ^ { 2 } y ^ { 7 }$ 
C)  $1,259,712 x ^ { 8 } y ^ { 9 }$ 
D)  $1,259,712 x ^ { 2 } y ^ { 2 }$ 
E)  $1,259,712 x ^ { 7 } y ^ { 7 }$

Question 11

Find the specified nth term in the expansion of the binomial.(Write the expansion in descending powers of x. ) $( x - 4 y ) ^ { 12 } , n = 3$

Accepted Answer

A)  $1,056 x ^ { 9 } y ^ { 2 }$ 
B)  $1,320 x ^ { 10 } y ^ { 2 }$ 
C)  $1,056 x ^ { 10 } y ^ { 2 }$ 
D)  $1,056 y ^ { 2 }$ 
E)  $220 x ^ { 1 } y ^ { 2 }$ 
A)  $1,056 x ^ { 9 } y ^ { 2 }$ 
B)  $1,320 x ^ { 10 } y ^ { 2 }$ 
C)  $1,056 x ^ { 10 } y ^ { 2 }$ 
D)  $1,056 y ^ { 2 }$ 
E)  $220 x ^ { 1 } y ^ { 2 }$

Question 12

Calculate the binomial coefficient.​ ${}_7 C _ { 4 }$ ​

Accepted Answer

A) 33 
B) 37 
C) 34 
D) 36 
E) 35 
A) 33 
B) 37 
C) 34 
D) 36 
E) 35

Question 13

Use the binomial theorem to expand the binomial.​ $\left( \frac { z } { 2 } + b \right) ^ { 4 }$ ​

Accepted Answer

A)  $z ^ { 4 } + z ^ { 3 } b + z ^ { 2 } b ^ { 2 } + z b ^ { 3 } + b ^ { 4 }$ 
B)  $\frac { 1 } { 8 } z ^ { 4 } + \frac { 1 } { 2 } z ^ { 3 } b + \frac { 3 } { 2 } z ^ { 2 } b ^ { 2 } + 2 z b ^ { 3 } + b ^ { 4 }$ 
C)  $\frac { 1 } { 2 } z ^ { 4 } + b ^ { 4 }$ 
D)  $\frac { 1 } { 16 } z ^ { 4 } + \frac { 1 } { 8 } z ^ { 3 } b + \frac { 1 } { 4 } z ^ { 2 } b ^ { 2 } + \frac { 1 } { 2 } z b ^ { 3 } + b ^ { 4 }$ 
E)  $\frac { 1 } { 16 } z ^ { 4 } + \frac { 1 } { 2 } z ^ { 3 } b + \frac { 3 } { 2 } z ^ { 2 } b ^ { 2 } + 2 z b ^ { 3 } + b ^ { 4 }$ 
A)  $z ^ { 4 } + z ^ { 3 } b + z ^ { 2 } b ^ { 2 } + z b ^ { 3 } + b ^ { 4 }$ 
B)  $\frac { 1 } { 8 } z ^ { 4 } + \frac { 1 } { 2 } z ^ { 3 } b + \frac { 3 } { 2 } z ^ { 2 } b ^ { 2 } + 2 z b ^ { 3 } + b ^ { 4 }$ 
C)  $\frac { 1 } { 2 } z ^ { 4 } + b ^ { 4 }$ 
D)  $\frac { 1 } { 16 } z ^ { 4 } + \frac { 1 } { 8 } z ^ { 3 } b + \frac { 1 } { 4 } z ^ { 2 } b ^ { 2 } + \frac { 1 } { 2 } z b ^ { 3 } + b ^ { 4 }$ 
E)  $\frac { 1 } { 16 } z ^ { 4 } + \frac { 1 } { 2 } z ^ { 3 } b + \frac { 3 } { 2 } z ^ { 2 } b ^ { 2 } + 2 z b ^ { 3 } + b ^ { 4 }$

Question 14

Use the Binomial Theorem to expand and simplify the expression.​ $( y - 3 ) ^ { 3 }$ ​

Accepted Answer

A)  $y ^ { 3 } + 9 y ^ { 2 } + 27 y + 27$ 
B)  $y ^ { 3 } - 9 y ^ { 2 } + 27 y - 27$ 
C)  $y ^ { 3 } - 9 y ^ { 2 } - 27 y - 27$ 
D)  $y ^ { 3 } + 9 y ^ { 2 } + 27 y - 27$ 
E)  $y ^ { 3 } + 9 y ^ { 2 } - 9 y + 27$ 
A)  $y ^ { 3 } + 9 y ^ { 2 } + 27 y + 27$ 
B)  $y ^ { 3 } - 9 y ^ { 2 } + 27 y - 27$ 
C)  $y ^ { 3 } - 9 y ^ { 2 } - 27 y - 27$ 
D)  $y ^ { 3 } + 9 y ^ { 2 } + 27 y - 27$ 
E)  $y ^ { 3 } + 9 y ^ { 2 } - 9 y + 27$

Question 15

Calculate the binomial coefficient: $\left( \begin{array} { l } 
6 \
2
\end{array} \right)$

Accepted Answer

A) 30 
B) 1 
C) 12 
D) 0 
E) 15 
A) 30 
B) 1 
C) 12 
D) 0 
E) 15

Question 16

Evaluate using Pascal's Triangle.​ ${ } _ { 12 } C _ { 4 }$ ​

Accepted Answer

A) 496 
B) 495 
C) 497 
D) 494 
E) 493 
A) 496 
B) 495 
C) 497 
D) 494 
E) 493

Question 17

Use the Binomial Theorem to expand the complex number.Simplify your result.​ $( 3 - i ) ^ { 5 }$ ​

Accepted Answer

A)  $405 i + 12$ 
B)  $90 i + 12$ 
C)  $316 i + 405$ 
D)  $- 12 - 316 i$ 
E)  $316 + 12 i$ 
A)  $405 i + 12$ 
B)  $90 i + 12$ 
C)  $316 i + 405$ 
D)  $- 12 - 316 i$ 
E)  $316 + 12 i$

Question 18

Calculate the binomial coefficient.​ ${ } _ { 18 } C _ { 0 }$ ​

Accepted Answer

A) 2 
B) 3 
C) 1 
D) 4 
E) 0 
A) 2 
B) 3 
C) 1 
D) 4 
E) 0

Question 19

Find the 3rd term in the binomial expansion.​ $( z + t ) ^ { 4 }$

Accepted Answer

The answer of Find the 3rd term in the binomial...

Question 20

Use the Binomial Theorem to expand and simplify the expression.​ $( 2 x - 5 y ) ^ { 5 }$ ​

Accepted Answer

A)  $32 x ^ { 5 } - 400 x ^ { 4 } y - 2000 x ^ { 3 } y ^ { 2 } - 5000 x ^ { 2 } y ^ { 3 } - 6250 x y ^ { 4 } - 3125$ 
B)  $32 x ^ { 5 } - 400 x ^ { 4 } y + 2000 x ^ { 3 } y ^ { 2 } + 5000 x ^ { 2 } y ^ { 3 } + 6250 x y ^ { 4 } + 3125$ 
C)  $32 x ^ { 5 } + 400 x ^ { 4 } y + 2000 x ^ { 3 } y ^ { 2 } - 5000 x ^ { 2 } y ^ { 3 } + 6250 x y ^ { 4 } - 3125$ 
D)  $32 x ^ { 5 } - 400 x ^ { 4 } y + 2000 x ^ { 3 } y ^ { 2 } - 5000 x ^ { 2 } y ^ { 3 } + 6250 x y ^ { 4 } - 3125$ 
E)  $32 x ^ { 5 } + 400 x ^ { 4 } y + 2000 x ^ { 3 } y ^ { 2 } - 5000 x ^ { 2 } y ^ { 3 } + 6250 x y ^ { 4 } + 3125$ 
A)  $32 x ^ { 5 } - 400 x ^ { 4 } y - 2000 x ^ { 3 } y ^ { 2 } - 5000 x ^ { 2 } y ^ { 3 } - 6250 x y ^ { 4 } - 3125$ 
B)  $32 x ^ { 5 } - 400 x ^ { 4 } y + 2000 x ^ { 3 } y ^ { 2 } + 5000 x ^ { 2 } y ^ { 3 } + 6250 x y ^ { 4 } + 3125$ 
C)  $32 x ^ { 5 } + 400 x ^ { 4 } y + 2000 x ^ { 3 } y ^ { 2 } - 5000 x ^ { 2 } y ^ { 3 } + 6250 x y ^ { 4 } - 3125$ 
D)  $32 x ^ { 5 } - 400 x ^ { 4 } y + 2000 x ^ { 3 } y ^ { 2 } - 5000 x ^ { 2 } y ^ { 3 } + 6250 x y ^ { 4 } - 3125$ 
E)  $32 x ^ { 5 } + 400 x ^ { 4 } y + 2000 x ^ { 3 } y ^ { 2 } - 5000 x ^ { 2 } y ^ { 3 } + 6250 x y ^ { 4 } + 3125$

Exam 56: The Binomial Theorem

Calculate the binomial coefficient.​ 29C29{ } _ { 29 } C _ { 29 }29​C29​ ​

Use the binomial theorem to expand the binomial.​ (a+b)4( a + b ) ^ { 4 }(a+b)4

Calculate the binomial coefficient: 11C8{ } _ { 11 } C _ { 8 }11​C8​

Use the Binomial Theorem to expand and simplify the expression.​ 2(x−5)4+5(x−5)22 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }2(x−5)4+5(x−5)2 ​

Use the Binomial Theorem to expand and simplify the expression.​ (y−3)5( y - 3 ) ^ { 5 }(y−3)5 ​

Use the Binomial Theorem to expand and simplify the expression.​ (2t−5)3( 2 \sqrt { t } - 5 ) ^ { 3 }(2t​−5)3 ​

Find the specified nth term in the expansion of the binomial.​ (5x−3y)12,n=10( 5 x - 3 y ) ^ { 12 } , n = 10(5x−3y)12,n=10 ​

Use the Binomial Theorem to expand and simplify the expression. (4x+5y)4( 4 x + 5 y ) ^ { 4 }(4x+5y)4

Find the specified nth term in the expansion of the binomial.​ (4x+3y)9,n=8( 4 x + 3 y ) ^ { 9 } , n = 8(4x+3y)9,n=8 ​

Find the specified nth term in the expansion of the binomial.(Write the expansion in descending powers of x. ) (x−4y)12,n=3( x - 4 y ) ^ { 12 } , n = 3(x−4y)12,n=3

Calculate the binomial coefficient.​ 7C4{}_7 C _ { 4 }7​C4​ ​

Use the binomial theorem to expand the binomial.​ (z2+b)4\left( \frac { z } { 2 } + b \right) ^ { 4 }(2z​+b)4 ​

Use the Binomial Theorem to expand and simplify the expression.​ (y−3)3( y - 3 ) ^ { 3 }(y−3)3 ​

Calculate the binomial coefficient: (62)\left( \begin{array} { l } 6 \\2\end{array} \right)(62​)

Evaluate using Pascal's Triangle.​ 12C4{ } _ { 12 } C _ { 4 }12​C4​ ​

Use the Binomial Theorem to expand the complex number.Simplify your result.​ (3−i)5( 3 - i ) ^ { 5 }(3−i)5 ​

Calculate the binomial coefficient.​ 18C0{ } _ { 18 } C _ { 0 }18​C0​ ​

Find the 3rd term in the binomial expansion.​ (z+t)4( z + t ) ^ { 4 }(z+t)4

Use the Binomial Theorem to expand and simplify the expression.​ (2x−5y)5( 2 x - 5 y ) ^ { 5 }(2x−5y)5 ​

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

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Calculate the binomial coefficient. ${ } _ { 29 } C _ { 29 }$

Use the binomial theorem to expand the binomial. $( a + b ) ^ { 4 }$

Calculate the binomial coefficient: ${ } _ { 11 } C _ { 8 }$

Use the Binomial Theorem to expand and simplify the expression. $2 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }$

Use the Binomial Theorem to expand and simplify the expression. $( y - 3 ) ^ { 5 }$

Use the Binomial Theorem to expand and simplify the expression. $( 2 \sqrt { t } - 5 ) ^ { 3 }$

Find the specified nth term in the expansion of the binomial. $( 5 x - 3 y ) ^ { 12 } , n = 10$

Use the Binomial Theorem to expand and simplify the expression. $( 4 x + 5 y ) ^ { 4 }$

Find the specified nth term in the expansion of the binomial. $( 4 x + 3 y ) ^ { 9 } , n = 8$

Find the specified nth term in the expansion of the binomial.(Write the expansion in descending powers of x. ) $( x - 4 y ) ^ { 12 } , n = 3$

Calculate the binomial coefficient. ${}_7 C _ { 4 }$

Use the binomial theorem to expand the binomial. $\left( \frac { z } { 2 } + b \right) ^ { 4 }$

Use the Binomial Theorem to expand and simplify the expression. $( y - 3 ) ^ { 3 }$

Calculate the binomial coefficient: $\left( \begin{array} { l } 6 \\2\end{array} \right)$

Evaluate using Pascal's Triangle. ${ } _ { 12 } C _ { 4 }$

Use the Binomial Theorem to expand the complex number.Simplify your result. $( 3 - i ) ^ { 5 }$

Calculate the binomial coefficient. ${ } _ { 18 } C _ { 0 }$

Find the 3rd term in the binomial expansion. $( z + t ) ^ { 4 }$

Use the Binomial Theorem to expand and simplify the expression. $( 2 x - 5 y ) ^ { 5 }$