Question 1

Use the Binomial Theorem to expand and simplify the expression.​ $( \sqrt { x } + 7 ) ^ { 3 }$ ​

Accepted Answer

A)  $x ^ { 3 / 2 } + 21 x + 147 x ^ { 2 } + 343$ 
B)  $x ^ { 3 / 2 } + 21 x - 147 x ^ { 1 / 2 } + 343$ 
C)  $x ^ { 3 } + 21 x + 147 x ^ { 1 / 2 } + 343$ 
D)  $x ^ { 3 } + 21 x ^ { 2 } + 147 x + 343$ 
E)  $x ^ { 3 / 2 } + 21 x + 147 x ^ { 1 / 2 } + 343$ 
A)  $x ^ { 3 / 2 } + 21 x + 147 x ^ { 2 } + 343$ 
B)  $x ^ { 3 / 2 } + 21 x - 147 x ^ { 1 / 2 } + 343$ 
C)  $x ^ { 3 } + 21 x + 147 x ^ { 1 / 2 } + 343$ 
D)  $x ^ { 3 } + 21 x ^ { 2 } + 147 x + 343$ 
E)  $x ^ { 3 / 2 } + 21 x + 147 x ^ { 1 / 2 } + 343$

Question 2

Calculate the binomial coefficient.​ $\left( \frac { 12 } { 8 } \right)$ ​

Accepted Answer

A) 496 
B) 493 
C) 498 
D) 497 
E) 495 
A) 496 
B) 493 
C) 498 
D) 497 
E) 495

Question 3

Evaluate using Pascal's triangle.​ $\left( \begin{array} { l } 
6 \
5
\end{array} \right)$ ​

Accepted Answer

A)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 720$ 
B)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 21$ 
C)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 56$ 
D)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 1$ 
E)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 6$ 
A)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 720$ 
B)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 21$ 
C)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 56$ 
D)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 1$ 
E)  $\left( \begin{array} { l } 
6 \
5
\end{array} \right) = 6$

Question 4

Evaluate using Pascal's triangle.Show your work. $\left( \frac { 5 } { 4 } \right)$

Accepted Answer

The answer of Evaluate using Pascal's triangle.Show your work. \(\left(...

Question 5

Calculate the binomial coefficient.​ ${ } _ { 6 } C _ { 4 }$ ​

Accepted Answer

A) 16 
B) 15 
C) 17 
D) 14 
E) 13 
A) 16 
B) 15 
C) 17 
D) 14 
E) 13

Question 6

Use the Binomial Theorem to expand and simplify the expression. $( 4 x + 3 y ) ^ { 4 }$

Accepted Answer

A)  $256 x ^ { 4 } + 768 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + 81 y ^ { 4 }$ 
B)  $256 x ^ { 4 } + 4 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + y ^ { 4 }$ 
C)  $256 x ^ { 4 } + 108 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + 81 y ^ { 4 }$ 
D)  $x ^ { 4 } + 768 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + 81 y ^ { 4 }$ 
E)  $256 x ^ { 4 } + 768 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 } + 81 y ^ { 4 }$ 
A)  $256 x ^ { 4 } + 768 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + 81 y ^ { 4 }$ 
B)  $256 x ^ { 4 } + 4 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + y ^ { 4 }$ 
C)  $256 x ^ { 4 } + 108 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + 81 y ^ { 4 }$ 
D)  $x ^ { 4 } + 768 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 432 x y ^ { 3 } + 81 y ^ { 4 }$ 
E)  $256 x ^ { 4 } + 768 x ^ { 3 } y + 864 x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 } + 81 y ^ { 4 }$

Question 7

Expand the binomial by using Pascal's Triangle to determine the coefficients.​ $( 2 t - s ) ^ { 5 }$ ​

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Use the Binomial Theorem to expand and simplify the expression. $\left( x ^ { 3 / 4 } + 1 \right) ^ { 4 }$

Accepted Answer

A)  $x ^ { 3 } + 1$ 
B)  $x ^ { 3 } + 4 x ^ { 9 / 7 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } + 1$ 
C)  $x ^ { 3 } + 4 x ^ { 9 / 4 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } + 1$ 
D)  $- x ^ { 3 } + 4 x ^ { 9 / 4 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } - 1$ 
E)  $x ^ { 3 } + 4 x ^ { 2 } + 6 x + 1$ 
A)  $x ^ { 3 } + 1$ 
B)  $x ^ { 3 } + 4 x ^ { 9 / 7 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } + 1$ 
C)  $x ^ { 3 } + 4 x ^ { 9 / 4 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } + 1$ 
D)  $- x ^ { 3 } + 4 x ^ { 9 / 4 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } - 1$ 
E)  $x ^ { 3 } + 4 x ^ { 2 } + 6 x + 1$

Question 10

Expand the expression in the difference quotient and simplify.​ $\frac { f ( x + h ) - f ( x ) } { h }$ Difference quotient $f ( x ) = ( x ) ^ { 3 }$ ​

Accepted Answer

A)  $\frac { 3 x ^ { 2 } + 3 x h + h ^ { 2 } } { h }$ 
B)  $3 x ^ { 2 } - 3 x h - h ^ { 2 }$ 
C)  $\frac { 3 x ^ { 2 } + 3 x h - h ^ { 2 } } { h }$ 
D)  $3 x ^ { 2 } + 3 x h - h ^ { 2 }$ 
E)  $3 x ^ { 2 } + 3 x h + h ^ { 2 }$ 
A)  $\frac { 3 x ^ { 2 } + 3 x h + h ^ { 2 } } { h }$ 
B)  $3 x ^ { 2 } - 3 x h - h ^ { 2 }$ 
C)  $\frac { 3 x ^ { 2 } + 3 x h - h ^ { 2 } } { h }$ 
D)  $3 x ^ { 2 } + 3 x h - h ^ { 2 }$ 
E)  $3 x ^ { 2 } + 3 x h + h ^ { 2 }$

Question 11

​Use the Binominal Theorem to expand the complex number.Simplify your result.​ $( 4 - 6 i ) ^ { 4 }$ ​

Accepted Answer

A) ​ $- 256 + 1536 i + 3456 + 3456 i ^ { 3 } - 1296$ 
B) ​ $256 + 1536 i - 3456 + 3456 i ^ { 3 } + 1296$ 
C) ​ $- 256 - 1536 i + 3456 - 3456 i ^ { 3 } - 1296$ 
D) ​ $256 - 1536 i - 3456 - 3456 i ^ { 3 } + 1296$ 
E) ​ $1296 - 3456 i - 3456 - 1536 i ^ { 3 } + 256$ 
A) ​ $- 256 + 1536 i + 3456 + 3456 i ^ { 3 } - 1296$ 
B) ​ $256 + 1536 i - 3456 + 3456 i ^ { 3 } + 1296$ 
C) ​ $- 256 - 1536 i + 3456 - 3456 i ^ { 3 } - 1296$ 
D) ​ $256 - 1536 i - 3456 - 3456 i ^ { 3 } + 1296$ 
E) ​ $1296 - 3456 i - 3456 - 1536 i ^ { 3 } + 256$

Question 12

Find the coefficient a of the term in the expansion of the binomial. Binomial Term $( x - 3 y ) ^ { 9 }$ $a x ^ { 5 } y ^ { 4 }$

Accepted Answer

A) a = 13 
B) a = 10206 
C) a = 45 
D) a = -19683 
E) a = 3024 
A) a = 13 
B) a = 10206 
C) a = 45 
D) a = -19683 
E) a = 3024

Question 13

Use the Binomial Theorem to expand and simplify the expression.​ $( 7 a + b ) ^ { 3 }$ ​

Accepted Answer

A)  $343 a ^ { 3 } - 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$ 
B)  $a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$ 
C)  $343 a ^ { 3 } + 147 a ^ { 2 } b - 21 a b ^ { 2 } + b ^ { 3 }$ 
D)  $343 a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } - b ^ { 3 }$ 
E)  $343 a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$ 
A)  $343 a ^ { 3 } - 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$ 
B)  $a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$ 
C)  $343 a ^ { 3 } + 147 a ^ { 2 } b - 21 a b ^ { 2 } + b ^ { 3 }$ 
D)  $343 a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } - b ^ { 3 }$ 
E)  $343 a ^ { 3 } + 147 a ^ { 2 } b + 21 a b ^ { 2 } + b ^ { 3 }$

Question 14

Find the coefficient a of the term in the expansion of the binomial.​ Binomial Terms
$( 2 x - 5 y ) ^ { 9 } ~a x ^ { 4 } y ^ { 5 }$ ​

Accepted Answer

A) -6,300,001 
B) -6,300,002 
C) -6,299,999 
D) -6,300,000 
E) -6,299,997 
A) -6,300,001 
B) -6,300,002 
C) -6,299,999 
D) -6,300,000 
E) -6,299,997

Question 15

Find the coefficient a of the term in the expansion of the binomial.​ Binomial Terms
$( 6 x - y ) ^ { 10 }~ a x ^ { 2 } y ^ { 8 }$ ​

Accepted Answer

A) 1,621 
B) 1,620 
C) 1,619 
D) 1,623 
E) 1,618 
A) 1,621 
B) 1,620 
C) 1,619 
D) 1,623 
E) 1,618

Question 16

Use the Binomial Theorem to expand and simplify the expression.​ $( 2 x + y ) ^ { 3 }$ ​

Accepted Answer

A)  $8 x ^ { 3 } - 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }$ 
B)  $8 x ^ { 3 } + 12 x ^ { 2 } y - 6 x y ^ { 2 } + y ^ { 3 }$ 
C)  $x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }$ 
D)  $8 x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }$ 
E)  $8 x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } - y ^ { 3 }$ 
A)  $8 x ^ { 3 } - 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }$ 
B)  $8 x ^ { 3 } + 12 x ^ { 2 } y - 6 x y ^ { 2 } + y ^ { 3 }$ 
C)  $x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }$ 
D)  $8 x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }$ 
E)  $8 x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } - y ^ { 3 }$

Question 17

Find the specified nth term in the expansion of the binomial.​ $( x - 8 y ) ^ { 5 } , n = 3$ ​

Accepted Answer

A)  $640 x ^ { 5 } y ^ { 3 }$ 
B)  $640 x ^ { 3 } y ^ { 2 }$ 
C)  $640 x ^ { 2 } y ^ { 2 }$ 
D)  $640 x ^ { 3 } y ^ { 3 }$ 
E)  $640 x ^ { 2 } y ^ { 3 }$ 
A)  $640 x ^ { 5 } y ^ { 3 }$ 
B)  $640 x ^ { 3 } y ^ { 2 }$ 
C)  $640 x ^ { 2 } y ^ { 2 }$ 
D)  $640 x ^ { 3 } y ^ { 3 }$ 
E)  $640 x ^ { 2 } y ^ { 3 }$

Question 18

Find the coefficient a of the term in the expansion of the binomial. Binomial Term $( 2 x - 5 y ) ^ { 8 }$ $a x ^ { 3 } y ^ { 5 }$

Accepted Answer

A)  $a = - 224000$ 
B)  $a = 336$ 
C)  $a = 40$ 
D)  $a = 8$ 
E)  $a = 390,625$ 
A)  $a = - 224000$ 
B)  $a = 336$ 
C)  $a = 40$ 
D)  $a = 8$ 
E)  $a = 390,625$

Question 19

Find the coefficient a of the term in the expansion of the binomial.​ Binomial Terms
$\left( x ^ { 2 } + 8 \right) ^ { 12 } a x ^ { 8 }$ ​

Accepted Answer

A) 8,304,721,920 
B) 8,304,721,921 
C) 8,304,721,923 
D) 8,304,721,918 
E) 8,304,721,919 
A) 8,304,721,920 
B) 8,304,721,921 
C) 8,304,721,923 
D) 8,304,721,918 
E) 8,304,721,919

Question 20

Evaluate using Pascal's triangle.​ ${ } _ { 7 } C _ { 4 }$ ​

Accepted Answer

A)  ${ } _ { 7 } C _ { 4 } = 840$ 
B)  ${ } _ { 7 } C _ { 4 } = 70$ 
C)  ${ } _ { 7 } C _ { 4 } = 126$ 
D)  ${ } _ { 7 } C _ { 4 } = 15$ 
E)  ${ } _ { 7 } C _ { 4 } = 35$ 
A)  ${ } _ { 7 } C _ { 4 } = 840$ 
B)  ${ } _ { 7 } C _ { 4 } = 70$ 
C)  ${ } _ { 7 } C _ { 4 } = 126$ 
D)  ${ } _ { 7 } C _ { 4 } = 15$ 
E)  ${ } _ { 7 } C _ { 4 } = 35$

Exam 56: The Binomial Theorem

Use the Binomial Theorem to expand and simplify the expression.​ (x+7)3( \sqrt { x } + 7 ) ^ { 3 }(x​+7)3 ​

Calculate the binomial coefficient.​ (128)\left( \frac { 12 } { 8 } \right)(812​) ​

Evaluate using Pascal's triangle.​ (65)\left( \begin{array} { l } 6 \\5\end{array} \right)(65​) ​

Evaluate using Pascal's triangle.Show your work. (54)\left( \frac { 5 } { 4 } \right)(45​)

Calculate the binomial coefficient.​ 6C4{ } _ { 6 } C _ { 4 }6​C4​ ​

Use the Binomial Theorem to expand and simplify the expression. (4x+3y)4( 4 x + 3 y ) ^ { 4 }(4x+3y)4

Expand the binomial by using Pascal's Triangle to determine the coefficients.​ (2t−s)5( 2 t - s ) ^ { 5 }(2t−s)5 ​

Use the binomial theorem to expand the binomial.​ (c+y)4( c + y ) ^ { 4 }(c+y)4 ​

Use the Binomial Theorem to expand and simplify the expression. (x3/4+1)4\left( x ^ { 3 / 4 } + 1 \right) ^ { 4 }(x3/4+1)4

Expand the expression in the difference quotient and simplify.​ f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​ Difference quotient f(x)=(x)3f ( x ) = ( x ) ^ { 3 }f(x)=(x)3 ​

​Use the Binominal Theorem to expand the complex number.Simplify your result.​ (4−6i)4( 4 - 6 i ) ^ { 4 }(4−6i)4 ​

Find the coefficient a of the term in the expansion of the binomial. Binomial Term (x−3y)9( x - 3 y ) ^ { 9 }(x−3y)9 ax5y4a x ^ { 5 } y ^ { 4 }ax5y4

Use the Binomial Theorem to expand and simplify the expression.​ (7a+b)3( 7 a + b ) ^ { 3 }(7a+b)3 ​

Find the coefficient a of the term in the expansion of the binomial.​ Binomial Terms (2x−5y)9 ax4y5( 2 x - 5 y ) ^ { 9 } ~a x ^ { 4 } y ^ { 5 }(2x−5y)9 ax4y5 ​

Find the coefficient a of the term in the expansion of the binomial.​ Binomial Terms (6x−y)10 ax2y8( 6 x - y ) ^ { 10 }~ a x ^ { 2 } y ^ { 8 }(6x−y)10 ax2y8 ​

Use the Binomial Theorem to expand and simplify the expression.​ (2x+y)3( 2 x + y ) ^ { 3 }(2x+y)3 ​

Find the specified nth term in the expansion of the binomial.​ (x−8y)5,n=3( x - 8 y ) ^ { 5 } , n = 3(x−8y)5,n=3 ​

Find the coefficient a of the term in the expansion of the binomial. Binomial Term (2x−5y)8( 2 x - 5 y ) ^ { 8 }(2x−5y)8 ax3y5a x ^ { 3 } y ^ { 5 }ax3y5

Find the coefficient a of the term in the expansion of the binomial.​ Binomial Terms (x2+8)12ax8\left( x ^ { 2 } + 8 \right) ^ { 12 } a x ^ { 8 }(x2+8)12ax8 ​

Evaluate using Pascal's triangle.​ 7C4{ } _ { 7 } C _ { 4 }7​C4​ ​

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

Use the Binomial Theorem to expand and simplify the expression. $( \sqrt { x } + 7 ) ^ { 3 }$

Calculate the binomial coefficient. $\left( \frac { 12 } { 8 } \right)$

Evaluate using Pascal's triangle. $\left( \begin{array} { l } 6 \\5\end{array} \right)$

Evaluate using Pascal's triangle.Show your work. $\left( \frac { 5 } { 4 } \right)$

Calculate the binomial coefficient. ${ } _ { 6 } C _ { 4 }$

Use the Binomial Theorem to expand and simplify the expression. $( 4 x + 3 y ) ^ { 4 }$

Expand the binomial by using Pascal's Triangle to determine the coefficients. $( 2 t - s ) ^ { 5 }$

Use the binomial theorem to expand the binomial. $( c + y ) ^ { 4 }$

Use the Binomial Theorem to expand and simplify the expression. $\left( x ^ { 3 / 4 } + 1 \right) ^ { 4 }$

Expand the expression in the difference quotient and simplify. $\frac { f ( x + h ) - f ( x ) } { h }$ Difference quotient $f ( x ) = ( x ) ^ { 3 }$

Use the Binominal Theorem to expand the complex number.Simplify your result. $( 4 - 6 i ) ^ { 4 }$

Find the coefficient a of the term in the expansion of the binomial. Binomial Term $( x - 3 y ) ^ { 9 }$ $a x ^ { 5 } y ^ { 4 }$

Use the Binomial Theorem to expand and simplify the expression. $( 7 a + b ) ^ { 3 }$

Find the coefficient a of the term in the expansion of the binomial. Binomial Terms $( 2 x - 5 y ) ^ { 9 } ~a x ^ { 4 } y ^ { 5 }$

Find the coefficient a of the term in the expansion of the binomial. Binomial Terms $( 6 x - y ) ^ { 10 }~ a x ^ { 2 } y ^ { 8 }$

Use the Binomial Theorem to expand and simplify the expression. $( 2 x + y ) ^ { 3 }$

Find the specified nth term in the expansion of the binomial. $( x - 8 y ) ^ { 5 } , n = 3$

Find the coefficient a of the term in the expansion of the binomial. Binomial Term $( 2 x - 5 y ) ^ { 8 }$ $a x ^ { 3 } y ^ { 5 }$

Find the coefficient a of the term in the expansion of the binomial. Binomial Terms $\left( x ^ { 2 } + 8 \right) ^ { 12 } a x ^ { 8 }$

Evaluate using Pascal's triangle. ${ } _ { 7 } C _ { 4 }$