Question 1

Add the polynomials and simplify. $$\left( 9 m ^ { 4 } + 8 m ^ { 3 } - 7 m \right) + \left( 7 m ^ { 4 } + 9 m ^ { 2 } + 5 m \right)$$

Accepted Answer

A)  $16 m ^ { 4 } + 8 m ^ { 3 } + 2 m ^ { 2 } + 5 m$ 
B)  $16 m ^ { 4 } + 8 m ^ { 3 } + 9 m ^ { 2 } - 12 m$ 
C)  $16 m ^ { 4 } + 8 m ^ { 3 } + 9 m ^ { 2 } - 2 m$ 
D)  $9 m ^ { 4 } + 7 m ^ { 3 } + 9 m ^ { 2 } - 2 m$ 
A)  $16 m ^ { 4 } + 8 m ^ { 3 } + 2 m ^ { 2 } + 5 m$ 
B)  $16 m ^ { 4 } + 8 m ^ { 3 } + 9 m ^ { 2 } - 12 m$ 
C)  $16 m ^ { 4 } + 8 m ^ { 3 } + 9 m ^ { 2 } - 2 m$ 
D)  $9 m ^ { 4 } + 7 m ^ { 3 } + 9 m ^ { 2 } - 2 m$

Question 2

$$\text { Given } P ( x ) = 3 x ^ { 2 } - 4 x + 7 , \text { find the function value }$$ P(-1)

Accepted Answer

A)  5 
B)  0 
C)  6 
D)  14 
A)  5 
B)  0 
C)  6 
D)  14

Question 3

Multiply the polynomials by using the distributive property. $$\left. \left( \frac { 5 } { 6 } x - 2 \right) - \frac { 1 } { 3 } x + 4 \right)$$

Accepted Answer

A)  $- \frac { 5 } { 18 } x ^ { 2 } + 4 x + 8$ 
B)  $- \frac { 5 } { 18 } x ^ { 2 } + 4 x - 8$ 
C)  $- \frac { 10 } { 3 } x ^ { 2 } + 4 x + 2$ 
D)  $- \frac { 5 } { 18 } x ^ { 2 } + \frac { 8 } { 3 } x - 8$ 
A)  $- \frac { 5 } { 18 } x ^ { 2 } + 4 x + 8$ 
B)  $- \frac { 5 } { 18 } x ^ { 2 } + 4 x - 8$ 
C)  $- \frac { 10 } { 3 } x ^ { 2 } + 4 x + 2$ 
D)  $- \frac { 5 } { 18 } x ^ { 2 } + \frac { 8 } { 3 } x - 8$

Question 4

Translate from algebraic form to English form. (m - n)(m + n)

Accepted Answer

A)  The product of the difference between m and n 
B)  The sum of the product of m minus n and the product of m and n 
C)  The product of the difference of m and n and the sum of m and n 
D)  The product of m minus n and the opposite of m minus n 
A)  The product of the difference between m and n 
B)  The sum of the product of m minus n and the product of m and n 
C)  The product of the difference of m and n and the sum of m and n 
D)  The product of m minus n and the opposite of m minus n

Question 5

Simplify the expression. $- 2 s ( - 5 s - 1 ) ( s - 4 )$

Accepted Answer

A)  $10 s ^ { 3 } + 19 s ^ { 2 } + 4 s$ 
B)  $10 s ^ { 3 } - 38 s ^ { 2 } - 8 s$ 
C)  $10 s ^ { 3 } - 38 s ^ { 2 } - 8$ 
D)  $10 s ^ { 3 } - 8 s$ 
A)  $10 s ^ { 3 } + 19 s ^ { 2 } + 4 s$ 
B)  $10 s ^ { 3 } - 38 s ^ { 2 } - 8 s$ 
C)  $10 s ^ { 3 } - 38 s ^ { 2 } - 8$ 
D)  $10 s ^ { 3 } - 8 s$

Question 6

Multiply by using the special case products. $\left( m ^ { 5 } + 6 n ^ { 3 } \right) \left( m ^ { 5 } - 6 n ^ { 3 } \right)$

Accepted Answer

A)  $m ^ { 10 } + 12 m ^ { 5 } n ^ { 3 } - 36 n ^ { 6 }$ 
B)  $m ^ { 10 } - 36 n ^ { 6 }$ 
C)  $m ^ { 10 } - 6 n ^ { 6 }$ 
D)  $m ^ { 10 } - 12 m ^ { 5 } n ^ { 3 } - 36 n ^ { 6 }$ 
A)  $m ^ { 10 } + 12 m ^ { 5 } n ^ { 3 } - 36 n ^ { 6 }$ 
B)  $m ^ { 10 } - 36 n ^ { 6 }$ 
C)  $m ^ { 10 } - 6 n ^ { 6 }$ 
D)  $m ^ { 10 } - 12 m ^ { 5 } n ^ { 3 } - 36 n ^ { 6 }$

Question 7

Factor by using substitution. $8 v ^ { 4 } - 31 v ^ { 2 } + 21$

Accepted Answer

A)  $\left( 8 v ^ { 2 } - 7 \right) \left( v ^ { 2 } - 3 \right)$ 
B)  $\left( 8 v ^ { 2 } - 3 \right) \left( v ^ { 2 } - 7 \right)$ 
C)  $\left( 8 v ^ { 2 } + 7 \right) \left( v ^ { 2 } + 3 \right)$ 
D)  Prime 
A)  $\left( 8 v ^ { 2 } - 7 \right) \left( v ^ { 2 } - 3 \right)$ 
B)  $\left( 8 v ^ { 2 } - 3 \right) \left( v ^ { 2 } - 7 \right)$ 
C)  $\left( 8 v ^ { 2 } + 7 \right) \left( v ^ { 2 } + 3 \right)$ 
D)  Prime

Question 8

How old (in whole years) is someone that has been alive for $1.6 \times 10 ^ { 4 }$ days?

Accepted Answer

The answer of How old (in whole years) is someone...

Question 9

A vacant lot in a housing development is in the shape of a triangle. The smallest side is 31 feet less than the middle side and the larger side is 15 feet less than 4 times the middle side. Find a function P that represents the perimeter in terms of x, where x represents the measure of the middle side.

Accepted Answer

A)  P(x) = 6x - 46 
B)  P(x) = 4x - 46 
C)  P(x) = 5x - 46 
D)  P(x) = 6x + 16 
A)  P(x) = 6x - 46 
B)  P(x) = 4x - 46 
C)  P(x) = 5x - 46 
D)  P(x) = 6x + 16

Question 10

Write the number in scientific notation.
432,000,000

Accepted Answer

The answer of Write the number in scientific notation.
432,000,000...

Question 11

The height of a triangle is 2 cm more than the base. If the height is increased by 2 cm while the base remains the same, the new area becomes 82.5 cm2. Find the base and the height of the original Triangle.

Accepted Answer

A)  base = 9 cm; height = 11 cm 
B)  base = 13 cm; height = 15 cm 
C)  base = 11 cm; height = 15 cm 
D)  base = 11 cm; height = 13 cm 
A)  base = 9 cm; height = 11 cm 
B)  base = 13 cm; height = 15 cm 
C)  base = 11 cm; height = 15 cm 
D)  base = 11 cm; height = 13 cm

Question 12

Add the polynomials and simplify. $$\begin{array} { l } 
2 q ^ { 3 } + 2 q + 4 \
+ \left( 5 q ^ { 3 } - 8 q ^ { 2 } + 7 q \right) \
\hline
\end{array}$$

Accepted Answer

A)  $7 q ^ { 3 } - 5 q + 4$ 
B)  $7 q ^ { 3 } - 8 q ^ { 2 } + 9 q + 4$ 
C)  $- 3 q ^ { 3 } + 8 q ^ { 2 } - 5 q + 4$ 
D)  $7 q ^ { 3 } - 8 q ^ { 2 } + 9$ 
A)  $7 q ^ { 3 } - 5 q + 4$ 
B)  $7 q ^ { 3 } - 8 q ^ { 2 } + 9 q + 4$ 
C)  $- 3 q ^ { 3 } + 8 q ^ { 2 } - 5 q + 4$ 
D)  $7 q ^ { 3 } - 8 q ^ { 2 } + 9$

Question 13

Factor completely. $$27 x ^ { 12 } + 64 y ^ { 12 }$$

Accepted Answer

A)  $\left( 3 x ^ { 4 } - 4 y ^ { 4 } \right) \left( 9 x ^ { 8 } + 12 x ^ { 4 } y ^ { 4 } + 16 y ^ { 8 } \right)$ 
B)  $\left( 3 x ^ { 4 } + 4 y ^ { 4 } \right) \left( 9 x ^ { 8 } - 12 x ^ { 4 } y ^ { 4 } + 16 y ^ { 8 } \right)$ 
C)  $\left( 3 x ^ { 4 } + 4 y ^ { 4 } \right) \left( 9 x ^ { 8 } + 12 x ^ { 4 } y ^ { 4 } + 16 y ^ { 8 } \right)$ 
D)  $\left( 3 x ^ { 4 } + 4 y ^ { 4 } \right) \left( 9 x ^ { 8 } - 24 x ^ { 4 } y ^ { 4 } + 16 y ^ { 8 } \right)$ 
A)  $\left( 3 x ^ { 4 } - 4 y ^ { 4 } \right) \left( 9 x ^ { 8 } + 12 x ^ { 4 } y ^ { 4 } + 16 y ^ { 8 } \right)$ 
B)  $\left( 3 x ^ { 4 } + 4 y ^ { 4 } \right) \left( 9 x ^ { 8 } - 12 x ^ { 4 } y ^ { 4 } + 16 y ^ { 8 } \right)$ 
C)  $\left( 3 x ^ { 4 } + 4 y ^ { 4 } \right) \left( 9 x ^ { 8 } + 12 x ^ { 4 } y ^ { 4 } + 16 y ^ { 8 } \right)$ 
D)  $\left( 3 x ^ { 4 } + 4 y ^ { 4 } \right) \left( 9 x ^ { 8 } - 24 x ^ { 4 } y ^ { 4 } + 16 y ^ { 8 } \right)$

Question 14

Factor completely. $$\frac { 64 } { 81 } r ^ { 2 } - \frac { 16 } { 25 } s ^ { 2 }$$

Accepted Answer

A)  $\left( \frac { 8 } { 9 } r + \frac { 4 } { 5 } s \left( \frac { 8 } { 9 } r - \frac { 4 } { 5 } s \right) \right.$ 
B)  $( r + s ) \left( \frac { 64 } { 81 } r - \frac { 16 } { 25 } s \right)$ 
C)  $\left( \frac { 8 } { 9 } r - \frac { 4 } { 5 } s \right) ^ { 2 }$ 
D)  $\left( \frac { 8 } { 9 } r + \frac { 4 } { 5 } s \right) ^ { 2 }$ 
A)  $\left( \frac { 8 } { 9 } r + \frac { 4 } { 5 } s \left( \frac { 8 } { 9 } r - \frac { 4 } { 5 } s \right) \right.$ 
B)  $( r + s ) \left( \frac { 64 } { 81 } r - \frac { 16 } { 25 } s \right)$ 
C)  $\left( \frac { 8 } { 9 } r - \frac { 4 } { 5 } s \right) ^ { 2 }$ 
D)  $\left( \frac { 8 } { 9 } r + \frac { 4 } { 5 } s \right) ^ { 2 }$

Question 15

Solve the equation. $$( 5 v + 1 ) ( 8 v - 2 ) = 0$$

Accepted Answer

A)  $v = - \frac { 1 } { 5 } ; v = \frac { 1 } { 4 }$ 
B)  $v = 0$ 
C)  $v = \frac { 1 } { 5 } ; v = \frac { 2 } { 5 }$ 
D)  $v = \frac { 1 } { 5 } ; v = - \frac { 2 } { 5 }$ 
A)  $v = - \frac { 1 } { 5 } ; v = \frac { 1 } { 4 }$ 
B)  $v = 0$ 
C)  $v = \frac { 1 } { 5 } ; v = \frac { 2 } { 5 }$ 
D)  $v = \frac { 1 } { 5 } ; v = - \frac { 2 } { 5 }$

Question 16

Determine whether the given function is a polynomial function. If it is a polynomial function, state the degree. If not, state the reason why. $$f ( x ) = - 4 | x | + \frac { 3 } { 7 }$$

Accepted Answer

A)  No, absolute value functions do not fit the form of a polynomial function. 
B)  Yes; degree:0 
C)  Yes; degree 1 
D)  Yes; degree: 2 
A)  No, absolute value functions do not fit the form of a polynomial function. 
B)  Yes; degree:0 
C)  Yes; degree 1 
D)  Yes; degree: 2

Question 17

Factor out the indicated quantity. $- 4 m n ^ { 3 } + 5 m n - 9 m$ : Factor out the quantity $- m$.

Accepted Answer

A)  $- m \left( - 4 n ^ { 3 } + 5 n - 9 \right)$ 
B)  $- m \left( 4 n ^ { 3 } - 5 n + 9 m \right)$ 
C)  $- m \left( 4 n ^ { 3 } - 5 n + 9 \right)$ 
D)  $- m \left( 4 n ^ { 3 } - 5 n - 9 \right)$ 
A)  $- m \left( - 4 n ^ { 3 } + 5 n - 9 \right)$ 
B)  $- m \left( 4 n ^ { 3 } - 5 n + 9 m \right)$ 
C)  $- m \left( 4 n ^ { 3 } - 5 n + 9 \right)$ 
D)  $- m \left( 4 n ^ { 3 } - 5 n - 9 \right)$

Question 18

Divide the polynomials. $\frac { - 20 x ^ { 6 } y ^ { 3 } + 50 x ^ { 5 } y ^ { 3 } - 2 x ^ { 3 } y ^ { 5 } } { - 10 x ^ { 5 } y ^ { 3 } }$

Accepted Answer

A)  $2 x - 5 y + \frac { y ^ { 2 } } { 5 x ^ { 2 } }$ 
B)  $2 x - 5 + \frac { 2 y ^ { 3 } } { 5 x ^ { 2 } }$ 
C)  $2 x - 5 + \frac { y ^ { 2 } } { 5 x ^ { 2 } }$ 
D)  $2 x - 5 + \frac { y ^ { 2 } } { 5 }$ 
A)  $2 x - 5 y + \frac { y ^ { 2 } } { 5 x ^ { 2 } }$ 
B)  $2 x - 5 + \frac { 2 y ^ { 3 } } { 5 x ^ { 2 } }$ 
C)  $2 x - 5 + \frac { y ^ { 2 } } { 5 x ^ { 2 } }$ 
D)  $2 x - 5 + \frac { y ^ { 2 } } { 5 }$

Question 19

The product of two consecutive even integers is 8. Find the integers.

Accepted Answer

A)  2, 4 or -4, -2 
B)  2, 4 or -2, 0 
C)  -4, -2 
D)  2, 4 
A)  2, 4 or -4, -2 
B)  2, 4 or -2, 0 
C)  -4, -2 
D)  2, 4

Question 20

Find the difference of $\left( 5 v ^ { 10 } - 2 v ^ { 6 } + 6 v ^ { 2 } \right)$ and $\left( 4 v ^ { 2 } + 7 v ^ { 6 } - 8 v + 4 \right)$.

Accepted Answer

A)  $5 v ^ { 10 } + 5 v ^ { 6 } + 10 v ^ { 2 } - 8 v + 4$ 
B)  $5 v ^ { 10 } - 9 v ^ { 6 } + 10 v ^ { 2 } + 8 v - 4$ 
C)  $5 v ^ { 10 } - 9 v ^ { 6 } + 2 v ^ { 2 } + 8 v - 4$ 
D)  $- 5 v ^ { 10 } + 9 v ^ { 6 } - 2 v ^ { 2 } - 8 v + 4$ 
A)  $5 v ^ { 10 } + 5 v ^ { 6 } + 10 v ^ { 2 } - 8 v + 4$ 
B)  $5 v ^ { 10 } - 9 v ^ { 6 } + 10 v ^ { 2 } + 8 v - 4$ 
C)  $5 v ^ { 10 } - 9 v ^ { 6 } + 2 v ^ { 2 } + 8 v - 4$ 
D)  $- 5 v ^ { 10 } + 9 v ^ { 6 } - 2 v ^ { 2 } - 8 v + 4$

Add the polynomials and simplify. $\left( 9 m ^ { 4 } + 8 m ^ { 3 } - 7 m \right) + \left( 7 m ^ { 4 } + 9 m ^ { 2 } + 5 m \right)$

$\text { Given } P ( x ) = 3 x ^ { 2 } - 4 x + 7 , \text { find the function value }$ P(-1)

Multiply the polynomials by using the distributive property. $\left. \left( \frac { 5 } { 6 } x - 2 \right) - \frac { 1 } { 3 } x + 4 \right)$

Translate from algebraic form to English form. (m - n)(m + n)

Simplify the expression. $- 2 s ( - 5 s - 1 ) ( s - 4 )$

Multiply by using the special case products. $\left( m ^ { 5 } + 6 n ^ { 3 } \right) \left( m ^ { 5 } - 6 n ^ { 3 } \right)$

Factor by using substitution. $8 v ^ { 4 } - 31 v ^ { 2 } + 21$

How old (in whole years) is someone that has been alive for $1.6 \times 10 ^ { 4 }$ days?

Write the number in scientific notation. 432,000,000

The height of a triangle is 2 cm more than the base. If the height is increased by 2 cm while the base remains the same, the new area becomes 82.5 cm². Find the base and the height of the original Triangle.

Add the polynomials and simplify. 2+2q+4 + 5-8+7q

Factor completely. $27 x ^ { 12 } + 64 y ^ { 12 }$

Factor completely. $\frac { 64 } { 81 } r ^ { 2 } - \frac { 16 } { 25 } s ^ { 2 }$

Solve the equation. $( 5 v + 1 ) ( 8 v - 2 ) = 0$

Determine whether the given function is a polynomial function. If it is a polynomial function, state the degree. If not, state the reason why. $f ( x ) = - 4 | x | + \frac { 3 } { 7 }$

Factor out the indicated quantity. $- 4 m n ^ { 3 } + 5 m n - 9 m$ : Factor out the quantity $- m$ .

Divide the polynomials. $\frac { - 20 x ^ { 6 } y ^ { 3 } + 50 x ^ { 5 } y ^ { 3 } - 2 x ^ { 3 } y ^ { 5 } } { - 10 x ^ { 5 } y ^ { 3 } }$

The product of two consecutive even integers is 8. Find the integers.

Find the difference of $\left( 5 v ^ { 10 } - 2 v ^ { 6 } + 6 v ^ { 2 } \right)$ and $\left( 4 v ^ { 2 } + 7 v ^ { 6 } - 8 v + 4 \right)$ .

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Exam 4: Polynomials

Add the polynomials and simplify. (9m4+8m3−7m)+(7m4+9m2+5m)\left( 9 m ^ { 4 } + 8 m ^ { 3 } - 7 m \right) + \left( 7 m ^ { 4 } + 9 m ^ { 2 } + 5 m \right)(9m4+8m3−7m)+(7m4+9m2+5m)

Given P(x)=3x2−4x+7, find the function value \text { Given } P ( x ) = 3 x ^ { 2 } - 4 x + 7 , \text { find the function value } Given P(x)=3x2−4x+7, find the function value P(-1)

Multiply the polynomials by using the distributive property. (56x−2)−13x+4)\left. \left( \frac { 5 } { 6 } x - 2 \right) - \frac { 1 } { 3 } x + 4 \right)(65​x−2)−31​x+4)

Translate from algebraic form to English form. (m - n)(m + n)

Simplify the expression. −2s(−5s−1)(s−4)- 2 s ( - 5 s - 1 ) ( s - 4 )−2s(−5s−1)(s−4)

Multiply by using the special case products. (m5+6n3)(m5−6n3)\left( m ^ { 5 } + 6 n ^ { 3 } \right) \left( m ^ { 5 } - 6 n ^ { 3 } \right)(m5+6n3)(m5−6n3)

Factor by using substitution. 8v4−31v2+218 v ^ { 4 } - 31 v ^ { 2 } + 218v4−31v2+21

How old (in whole years) is someone that has been alive for 1.6×1041.6 \times 10 ^ { 4 }1.6×104 days?

Write the number in scientific notation. 432,000,000

The height of a triangle is 2 cm more than the base. If the height is increased by 2 cm while the base remains the same, the new area becomes 82.5 cm2. Find the base and the height of the original Triangle.

Add the polynomials and simplify. 2+2q+4 + 5-8+7q

Factor completely. 27x12+64y1227 x ^ { 12 } + 64 y ^ { 12 }27x12+64y12

Factor completely. 6481r2−1625s2\frac { 64 } { 81 } r ^ { 2 } - \frac { 16 } { 25 } s ^ { 2 }8164​r2−2516​s2

Solve the equation. (5v+1)(8v−2)=0( 5 v + 1 ) ( 8 v - 2 ) = 0(5v+1)(8v−2)=0

Determine whether the given function is a polynomial function. If it is a polynomial function, state the degree. If not, state the reason why. f(x)=−4∣x∣+37f ( x ) = - 4 | x | + \frac { 3 } { 7 }f(x)=−4∣x∣+73​

Factor out the indicated quantity. −4mn3+5mn−9m- 4 m n ^ { 3 } + 5 m n - 9 m−4mn3+5mn−9m : Factor out the quantity −m- m−m .

Divide the polynomials. −20x6y3+50x5y3−2x3y5−10x5y3\frac { - 20 x ^ { 6 } y ^ { 3 } + 50 x ^ { 5 } y ^ { 3 } - 2 x ^ { 3 } y ^ { 5 } } { - 10 x ^ { 5 } y ^ { 3 } }−10x5y3−20x6y3+50x5y3−2x3y5​

The product of two consecutive even integers is 8. Find the integers.

Find the difference of (5v10−2v6+6v2)\left( 5 v ^ { 10 } - 2 v ^ { 6 } + 6 v ^ { 2 } \right)(5v10−2v6+6v2) and (4v2+7v6−8v+4)\left( 4 v ^ { 2 } + 7 v ^ { 6 } - 8 v + 4 \right)(4v2+7v6−8v+4) .

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Add the polynomials and simplify. $\left( 9 m ^ { 4 } + 8 m ^ { 3 } - 7 m \right) + \left( 7 m ^ { 4 } + 9 m ^ { 2 } + 5 m \right)$

$\text { Given } P ( x ) = 3 x ^ { 2 } - 4 x + 7 , \text { find the function value }$ P(-1)

Multiply the polynomials by using the distributive property. $\left. \left( \frac { 5 } { 6 } x - 2 \right) - \frac { 1 } { 3 } x + 4 \right)$

Simplify the expression. $- 2 s ( - 5 s - 1 ) ( s - 4 )$

Multiply by using the special case products. $\left( m ^ { 5 } + 6 n ^ { 3 } \right) \left( m ^ { 5 } - 6 n ^ { 3 } \right)$

Factor by using substitution. $8 v ^ { 4 } - 31 v ^ { 2 } + 21$

How old (in whole years) is someone that has been alive for $1.6 \times 10 ^ { 4 }$ days?

The height of a triangle is 2 cm more than the base. If the height is increased by 2 cm while the base remains the same, the new area becomes 82.5 cm². Find the base and the height of the original Triangle.

Factor completely. $27 x ^ { 12 } + 64 y ^ { 12 }$

Factor completely. $\frac { 64 } { 81 } r ^ { 2 } - \frac { 16 } { 25 } s ^ { 2 }$

Solve the equation. $( 5 v + 1 ) ( 8 v - 2 ) = 0$

Determine whether the given function is a polynomial function. If it is a polynomial function, state the degree. If not, state the reason why. $f ( x ) = - 4 | x | + \frac { 3 } { 7 }$

Factor out the indicated quantity. $- 4 m n ^ { 3 } + 5 m n - 9 m$ : Factor out the quantity $- m$ .

Divide the polynomials. $\frac { - 20 x ^ { 6 } y ^ { 3 } + 50 x ^ { 5 } y ^ { 3 } - 2 x ^ { 3 } y ^ { 5 } } { - 10 x ^ { 5 } y ^ { 3 } }$

Find the difference of $\left( 5 v ^ { 10 } - 2 v ^ { 6 } + 6 v ^ { 2 } \right)$ and $\left( 4 v ^ { 2 } + 7 v ^ { 6 } - 8 v + 4 \right)$ .