Deck 5: Exponents and Polynomials

Question 1

In the expression , what is the base and the exponent?

Answer 1

2, 15

Question 2

Simplify the expression. $$\left( 2 y ^ { 2 } \right) ^ { 4 }$$

A) $16 y ^ { 6 }$
B) $16 y ^ { 8 }$
C) $2 y ^ { 8 }$
D) $16 y ^ { 4 }$
E) $2 y ^ { 2 }$

Answer 2

$16 y ^ { 8 }$

Question 3

Simplify the following expression. Do not use parentheses or negative exponents. $- ( - 9 ) ^ { - 2 }$

A)81
B)-81
C)-18
D) $\frac { 1 } { 81 }$
E) $- \frac { 1 } { 81 }$

Answer 3

$- \frac { 1 } { 81 }$

Question 4

Simplify the following expression. Assume that $$y \neq 0$$ . $$\frac { 8 y ^ { 4 } \cdot y ^ { 6 } \cdot y ^ { 6 } } { 2 \left( y ^ { 4 } \right) ^ { 3 } }$$

A) $4 y ^ { 137 }$
B) $4 y ^ { 4 }$
C) $6 y ^ { 4 }$
D) $4 y ^ { 9 }$
E) $8 y ^ { 4 }$

Question 5

Simplify the expression. $$\left( 2 y ^ { 6 } c ^ { 9 } \right) ^ { 2 }$$

A) $4 y ^ { 12 } c ^ { 18 }$
B) $2 y ^ { 8 } c ^ { 11 }$
C) $4 y ^ { 6 } c ^ { 9 }$
D) $4 y ^ { 8 } c ^ { 11 }$
E) $2 y ^ { 12 } c ^ { 18 }$

Question 6

Write the expression without using exponents. $19.3 c ^ { 0 }$

A)1
B)19.3
C)-19.3
D)0

Question 7

Simplify the following expression. $$x ^ { 4 } \cdot x ^ { 2 } \left( x ^ { 4 } \cdot x ^ { 2 } \right) \left( x ^ { 4 } \cdot x ^ { 2 } \right)$$

A) $x ^ { 6 }$
B) $x ^ { 8 }$
C) $6 x ^ { 16 }$
D) $x ^ { 16 }$
E) $x ^ { 18 }$

Question 8

Question 9

Write the expression without using exponents. ( -0.4797 ) $0$

A)0
B)-0.4797
C)-0.735
D)1

Question 10

Write the following expression as an expression involving only one base and one exponent. $$\left( 4 s ^ { 3 } s ^ { 4 } s ^ { 3 } \right) ^ { 2 }$$

A) $16 s ^ { 10 }$
B) $16 s ^ { 8 }$
C) $4 s ^ { 20 }$
D) $16 s ^ { 12 }$
E) $16 s ^ { 20 }$

Question 11

Simplify. $$\left( 15 ^ { 5 } \right) ^ { 3 }$$

A) $15 ^ { 15 }$
B) $15 ^ { 5 }$
C) $15 ^ { 3 }$
D) $15 ^ { 8 }$

Question 12

Simplify by writing the expression without using parentheses. $$\left( \frac { a ^ { 3 } a ^ { 2 } } { a ^ { 6 } } \right) ^ { 6 }$$

A) $\frac { 1 } { a }$
B) $\frac { 1 } { a ^ { 6 } }$
C) $\frac { 1 } { a ^ { 6 } }$ .
D) $\frac { 1 } { 6 a ^ { 6 } }$
E) $a ^ { 6 }$

Question 13

Simplify the expression. $$\left( s ^ { 5 } s ^ { 4 } \right) ^ { 2 }$$

A) $s ^ { 28 }$
B) $s ^ { 22 }$
C) $s ^ { 18 }$
D) $s ^ { 8 }$
E) $s ^ { 11 }$

Question 14

In the expression -9², what is the base?

Question 15

Simplify the following expression. $$\left( \frac { 2 a ^ { 2 } \cdot a ^ { 3 } \cdot a ^ { 6 } } { 3 a ^ { 3 } \cdot a ^ { 2 } } \right) ^ { 3 }$$

A) $\frac { 8 a ^ { 18 } } { 27 }$
B) $\frac { 8 a ^ { 24 } } { 27 }$
C) $\frac { 2 a ^ { 11 } } { 3 a ^ { 5 } }$
D) $\frac { 2 a ^ { 18 } } { 3 }$
E) $\frac { 8 a ^ { 18 } } { 3 a ^ { 5 } }$

Question 16

In the expression , what is the exponent?

Question 17

Write the expression without using exponents. $$( - 17 ) ^ { 0 }$$

A)0
B)-17
C)17
D)1

Question 18

Simplify the following expression. $$x ^ { 6 } \cdot x ^ { 2 }$$

A) $x ^ { 4 }$
B) $x ^ { 12 }$
C) $2 x ^ { 36 }$
D) $x ^ { 36 }$
E) $x ^ { 8 }$

Question 19

Write the following expression without using a negative exponent. $( - 32 ) ^ { - 1 }$

A)1
B)32
C) $- \frac { 1 } { 32 }$
D)-32
E) $\frac { 1 } { 32 }$

Question 20

Select the expression that completes the formula below. $$( x y ) ^ { k }$$

A) $x ^ { k } y ^ { k }$
B) $x ^ { m + k }$
C) $x ^ { m k }$
D) $\frac { x ^ { k } } { y ^ { k } }$
E)None of these

Question 21

The distance between the Sun and Mars is approximately $1.14 \times 10 ^ { 8 }$ miles. Use scientific notation to express this distance in feet. ( Hint: 5,280 feet = 1 mile.)

A) $601.92 \times 10 ^ { 9 }$ ft
B) $0.60192 \times 10 ^ { 12 }$ ft
C) $6.0192 \times 10 ^ { 12 }$ ft
D) $6.0192 \times 10 ^ { 11 }$ ft
E) $60.192 \times 10 ^ { 10 }$ ft

Question 22

Simplify the following expression. $$\frac { 1 } { 2 ^ { - 2 } }$$

A) $- 4$
B) $\frac { 1 } { 4 }$
C) $- \frac { 1 } { 4 }$
D) $4$
E)1

Question 23

Simplify the following expression. Do not use parentheses or negative exponents. $$\left( c ^ { 5 } y ^ { 4 } \right) ^ { - 8 }$$

A) $- \frac { 1 } { c ^ { 40 } y ^ { 32 } }$
B) $c ^ { 40 } y ^ { 32 }$
C) $c ^ { - 3 } y ^ { - 4 }$
D) $\frac { 1 } { c ^ { 40 } y ^ { 32 } }$
E) $- c ^ { 40 } y ^ { 32 }$

Question 24

Write the number in ordinary decimal notation. For example (2.78)(10) ⁴ = 27,800.

A)215,000
B)2,150,000
C)2,150
D)215
E)21,500

Question 25

Simplify the following expression. Do not use parentheses or negative exponents. $7 ^ { - 2 } \cdot 7 ^ { 3 } \cdot 7 ^ { - 4 }$

A)-343
B) $7 ^ { 3 }$
C) $\frac { 1 } { 343 }$
D) $- \frac { 1 } { 343 }$
E)343

Question 26

Write the number 55,000,000 in scientific notation.

A) $55 \times 10 ^ { 7 }$
B) $55 \times 10 ^ { 8 }$
C) $5.5 \times 10 ^ { 6 }$
D) $55 \times 10 ^ { 6 }$
E) $5.5 \times 10 ^ { 7 }$

Question 27

Write the number $53.5 \times 10 ^ { 3 }$ in scientific notation.

A) $535 \times 10 ^ { 2 }$
B)53,500
C) $5.35 \times 10 ^ { 3 }$
D) $5.35 \times 10 ^ { 4 }$
E) $5.35 \times 10 ^ { 5 }$

Question 28

The number 26,300,000,000,000 is written in __________ notation. And the number $2.63 \times 10 ^ { 13 }$ is written in __________ notation

A)standard; scientific
B)decimal; standard
C)standard; decimal
D)scientific; standard

Question 29

Simplify the following expression. $$\left( \frac { - 2 m ^ { 3 } m ^ { - 6 } } { m ^ { - 3 } m ^ { 6 } } \right) ^ { 2 }$$

A) $4 m ^ { 12 }$
B) $\frac { 1 } { 4 m ^ { 12 } }$
C) $- \frac { 4 } { m ^ { 12 } }$
D) $\frac { - 4 } { m ^ { 12 } }$
E) $\frac { 4 } { m ^ { 12 } }$

Question 30

Write the number 0.00052 in scientific notation.

A) $52 \times 10 ^ { - 4 }$
B) $5.2 \times 10 ^ { - 6 }$
C) $52 \times 10 ^ { - 5 }$
D) $5.2 \times 10 ^ { - 4 }$
E) $5.2 \times 10 ^ { - 5 }$

Question 31

The distance between two planets is approximately $4.2 \times 10 ^ { 7 }$ miles. Use scientific notation to express this distance in feet. (5,280 feet = 1 mile.)

A) $2.2586 \times 10 ^ { 13 }$ ft
B) $2.2176 \times 10 ^ { 11 }$ ft
C) $2.2306 \times 10 ^ { 9 }$ ft
D) $2.218 \times 10 ^ { 12 }$ ft
E) $2.0866 \times 10 ^ { 10 }$ ft

Question 32

Simplify the following expression. Do not use parentheses or negative exponents in your answer. $$\frac { x ^ { 14 } x ^ { - 5 } } { x ^ { 4 } x ^ { 2 } }$$

A) $x ^ { 4 }$
B) $x ^ { 3 }$
C) $x ^ { - 4 }$
D) $x ^ { - 3 }$
E) $x ^ { 5 }$

Question 33

Simplify the following expression. $$d ^ { ( 8 n + 8 ) } d ^ { ( - 5 n ) }$$

A) $d ^ { ( - 3 n + 8 ) }$
B) $d ^ { - ( 3 n + 8 ) }$
C) $d ^ { ( - ( 8 n + 8 ) 5 n ) }$
D) $d ^ { ( 11 n ) }$
E) $d ^ { ( 3 n + 8 ) }$

Question 34

Simplify the following expression. $$\left( \frac { 9 } { 16 } \right) ^ { - 1 }$$

A) $\frac { 9 } { 16 }$
B) $- \frac { 9 } { 16 }$
C)1
D) $\frac { 16 } { 9 }$
E) $- \frac { 16 } { 9 }$

Question 35

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in ordinary decimal notation. (0.00005)(1,100,000)

A)550
B)55
C)11.5
D)610
E)61

Question 36

Write the following expression with a single exponent. Assume there is no division by 0. $$\frac { b ^ { 9 m } } { b ^ { 7 m } }$$

A) $b ^ { 16 m }$
B) $b ^ { 2 m }$
C) $b ^ { 63 m }$
D) $\frac { 1 } { b ^ { 2 m } }$
E) $b ^ { - 2 m }$

Question 37

How much money should a young married couple invest now at a(n)6% annual rate if they want to have $100,000 in the bank when they reach retirement age in 40 years? Use the formula: where P is the amount of money to be invested at an annual rate i (expressed as a decimal)in order to have $ A in n years. Round your answer to the nearest integer. $ __________

Question 38

Write the number in ordinary decimal notation. For example, (2.78)(10) ⁴ = 27,800.

A)0.113
B)0.0113
C)0.00113
D)113
E)1,130

Question 39

Simplify the following expression. $$\frac { 2 ^ { - 3 } } { 3 ^ { - 1 } }$$

A)1
B) $\frac { 3 } { 8 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 8 } { 3 }$
E) $- \frac { 3 } { 8 }$

Question 40

Write the number in ordinary decimal notation. For example, (2.78)(10) ⁴ = 27,800.

A)550
B)55,000,000
C)5,500,000
D)5,500,000,000
E).0000000550

Question 41

Evaluate 7 x - 4 for x = - 3.

A)- 24
B)- 23
C)28
D)- 25
E)21

Question 42

The degree of a polynomial is the same as

A)the number of terms
B)the number of variables
C)the sum of the degrees in all terms
D)the degree of its term with largest degree
E)the degree of its term with least degree

Question 43

Subtract. $$\begin{array} { r } 6 x ^ { 2 } - 6 x + 6 \\3 x ^ { 2 } - 3 x - 5\\\hline \end{array}$$

A) $3 x ^ { 2 } - 3 x + 11$
B) $3 x ^ { 2 } - 3 x - 1$
C) $6 x ^ { 2 } - 3 x + 1$
D) $3 x ^ { 2 } - 3 x + 1$
E) $6 x ^ { 2 } - 3 x + 11$

Question 44

Simplify the expression. 3 y ( xy + y )- 5 y ²( x - 2 + 3 y )+ 2( y ³ + y ²)

A)- 2 xy ² + 13 y ² + 12 y ³
B)- 2 xy ² + 15 y ² - 13 y ³
C)8 xy ² + 13 y ² - 13 y ³
D)2 xy ² + 13 y ² - 12 y ³
E)none of these

Question 45

Evaluate $- x ^ { 2 } - 4$ for $x = - 1$ .

A)-7
B)-4
C)5
D)-3
E)-5

Question 46

Simplify the expression. $$( 5 x + 7 ) + ( 3 x - 6 )$$

A) $8 x + 1$
B) $8 x - 1$
C) $8 x + 7$
D) $5 x + 1$
E)none of these

Question 47

Simplify the expression. $$- 4 x y ^ { 2 } ( 5 x + 5 y + 3 z ) - 2 x \left( x y ^ { 2 } - 4 y ^ { 2 } z \right) - 2 y \left( 8 x y ^ { 2 } - 1 \right)$$

A) $- 18 x ^ { 2 } y ^ { 2 } - 20 x y ^ { 2 } z - 36 x y ^ { 3 } + 2 y$
B) $- 22 x ^ { 2 } y ^ { 2 } - 20 x y ^ { 2 } z + 36 x y ^ { 3 } + 2 y$
C) $- 22 x ^ { 2 } y ^ { 2 } - 4 x y ^ { 2 } z - 36 x y ^ { 3 } + 2 y$
D) $- 22 x ^ { 2 } y ^ { 2 } - 20 x y ^ { 2 } z - 36 x y ^ { 3 } + 2 y$
E)none of these

Question 48

Add the monomials. $$3 x ^ { 2 } + 5 x ^ { 2 }$$

A)8
B) $8 x ^ { 4 }$
C) $8 x ^ { 2 }$
D) $7 x ^ { 2 }$
E) $15 x ^ { 2 }$

Question 49

Evaluate the algebraic expression for the given values of the variables.

Question 50

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in ordinary decimal notation. $\frac { ( 480,000 ) ( 0.036 ) } { ( 0.0009 ) ( 600 ) }$

A)3,200
B)32
C)115,200,000
D)32,000
E)11,520,000,000

Question 51

Combine the like terms. 7 y and 6 y

A)13 y
B)15 y
C)12 y
D)13
E)42 y

Question 52

Simplify the expression. $$\left( 13 a ^ { 2 } + 6 a + 9 \right) + \left( 8 a ^ { 2 } + 9 a + 1 \right)$$

A) $21 a ^ { 2 } + 6 a + 10$
B) $21 a ^ { 2 } + 15 a + 10$
C) $21 a ^ { 2 } + 15 a$
D) $13 a ^ { 2 } + 15 a + 10$
E)none of these

Question 53

Subtract. $$\begin{array} { l } 3 x ^ { 3 } + 4 x ^ { 2 } - 5 x + 6 \\4 x ^ { 3 } - 3 x ^ { 2 } - 8 x - 1\\\hline \end{array}$$

A) $- x ^ { 3 } - x ^ { 2 } + 13 x + 7$
B) $- x ^ { 3 } + 7 x ^ { 2 } + 3 x + 7$
C) $x ^ { 3 } - 7 x ^ { 2 } - 13 x + 7$
D) $x ^ { 3 } - 7 x ^ { 2 } + 13 x + 7$
E) $- x ^ { 3 } - x ^ { 2 } - 13 x + 7$

Question 54

Simplify the expression. $( 19 x - 11 y ) - ( 3 x + 9 y )$

A) $22 x - 2 y$
B) $16 x - 2 y$
C) $16 x - 20 y$
D) $22 x - 20 y$
E)none of these

Question 55

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in scientific notation.

A)6 ¹³
B)(6)(10) ¹³
C)6 ^-13
D)(6)(10) ^-13
E)(6)(10) ¹¹

Question 56

Simplify the expression. $$6 \left( x ^ { 2 } - 9 x - 8 \right) - 5 \left( x ^ { 2 } - 9 x - 8 \right) + 8 \left( x ^ { 2 } - 9 x - 8 \right)$$

A) $9 x ^ { 2 } - 171 x - 152$
B) $9 x ^ { 2 } - 171 x - 72$
C) $9 x ^ { 2 } - 81 x - 72$
D) $9 x ^ { 2 } - 81 x - 152$
E)none of these

Question 57

Add the monomials. 8 b + 5 b + 2 b

Question 58

How many terms are contained in a monomial?

A)4
B)2
C)5
D)3
E)1

Question 59

Classify the following polynomial as a monomial, a binomial, or a trinomial. $- 9 b ^ { 2 } + 2 b - 5$

A)trinomial
B)monomial
C)binomial
D)none of these

Question 60

Find the sum when $8 x ^ { 2 } + 3 x - 3$ is added to the sum of $- 2 x ^ { 2 } - 7 x + 4$ and $- 9 x ^ { 2 } + 8 x - 4$ .

A) $15 x ^ { 2 } - 4 x - 3$
B) $- 3 x ^ { 2 } + 4 x + 5$
C) $- 3 x ^ { 2 } - 12 x + 5$
D) $- 3 x ^ { 2 } + 4 x - 3$
E)none of these

Question 61

Add the monomials.

Question 62

Solve the equation. $( t + 2 ) ( t + 6 ) = t ^ { 2 } - 4$

A)4
B)0
C)-2
D)8

Question 63

Subtract the monomials. $6 a ^ { 3 } - 3 a ^ { 3 }$

A)3
B) $3 a ^ { 3 }$
C) $4 a ^ { 3 }$
D) $- 18 a ^ { 3 }$
E) $18 a ^ { 3 }$

Question 64

Find the indicated product. ( a + 8 b )( x + y )

A)ax + 10 bx + ay + 9 by
B)ax + 8 bx + ay + by
C)ax + 8 bx + ay + 8 by
D)ax + 9 bx + ay + 8 by
E)ax + bx + ay + 9 by

Question 65

Solve the equation. $( t + 1 ) ( t + 9 ) = ( t + 4 ) ( t + 6 )$

A)5
B)0
C)3
D)15

Question 66

Find the product. $\left( - 2 a ^ { 2 } b \right) \left( - 2 a ^ { 3 } b ^ { 2 } \right) ( 5 a - 7 b )$

A) $14 a ^ { 5 } b ^ { 4 } - 10 a ^ { 6 } b ^ { 3 }$
B) $20 a ^ { 5 } b ^ { 3 } + 28 a ^ { 5 } b ^ { 4 }$
C) $20 a ^ { 6 } b ^ { 3 } - 28 a ^ { 5 } b ^ { 4 }$
D) $28 a ^ { 5 } b ^ { 4 } - 20 a ^ { 6 } b ^ { 3 }$
E) $10 a ^ { 6 } b ^ { 3 } - 14 a ^ { 5 } b ^ { 4 }$

Question 67

Find the product.

Question 68

Find the product. $$( 4 a + t ) ^ { 2 }$$

A) $16 a ^ { 2 } + 8 a t + t ^ { 2 }$
B) $22 a ^ { 2 } + 16 a t + t ^ { 2 }$
C) $24 a ^ { 2 } + 10 a t + t ^ { 2 }$
D) $19 a ^ { 2 } + 11 a t + t ^ { 2 }$
E) $25 a ^ { 2 } + 13 a t + t ^ { 2 }$

Question 69

Find the product. $\left( 3 t ^ { 6 } z ^ { 6 } \right) \left( 2 t ^ { 2 } z ^ { 2 } \right)$

A) $8 t ^ { 9 } z ^ { 9 }$
B) $6 t ^ { 8 } z$
C) $6 t ^ { 4 } z ^ { 4 }$
D) $6 t ^ { 12 } z ^ { 12 }$
E) $5 t ^ { 8 } z$

Question 70

Find the product. $$( z + 5 ) ( z - 5 )$$

A) $z ^ { 2 } - 24$
B) $z ^ { 2 } - 26$
C) $z ^ { 2 } - 25$
D) $z ^ { 2 } - 22$
E) $z ^ { 2 } - 23$

Question 71

Find the product. $\left( 2 s ^ { 5 } x ^ { 5 } \right) \left( 3 s ^ { 2 } x ^ { 3 } \right) ( s x )$

A) $5 s ^ { 7 } x ^ { 8 }$
B) $6 s ^ { 8 } x ^ { 9 }$
C) $6 s ^ { 10 } x ^ { 15 }$
D) $6 s ^ { 3 } x ^ { 2 }$
E)none of these

Question 72

Subtract the monomials. $9 a ^ { 6 } - 2 a ^ { 6 } - 2 a ^ { 6 }$

A) $6 a ^ { 6 }$
B)5
C) $16 a ^ { 6 }$
D) $5 a ^ { 6 }$
E) $36 a ^ { 6 }$

Question 73

Find the indicated product by applying the distributive property and combining similar terms. $$( x + 5 ) \left( x ^ { 2 } - 2 x - 7 \right)$$

A) $x ^ { 3 } + 3 x ^ { 2 } - 17 x - 35$
B) $x ^ { 3 } + 3 x ^ { 2 } - 17 x - 5$
C) $x ^ { 3 } + 5 x ^ { 2 } - 17 x - 35$
D) $x ^ { 3 } + 3 x ^ { 2 } - 17 x + 35$
E) $x ^ { 3 } + 3 x ^ { 2 } - 10 x - 35$

Question 74

Find the product. $\frac { 4 } { 3 } a ^ { 2 } b ( 6 a - 5 b )$

A) $\frac { 8 } { 3 } a ^ { 2 } b - \frac { 20 } { 3 } a ^ { 2 } b ^ { 2 }$
B) $\frac { 8 } { 3 } a ^ { 3 } b + \frac { 20 } { 3 } a ^ { 2 } b ^ { 2 }$
C) $8 a ^ { 3 } b - \frac { 20 } { 3 } a ^ { 2 } b ^ { 2 }$
D) $8 a ^ { 3 } b - \frac { 16 } { 3 } a b ^ { 2 }$
E) $8 a ^ { 2 } b + \frac { 20 } { 3 } a ^ { 2 } b ^ { 2 }$

Question 75

Find the indicated product by applying the distributive property and combining similar terms. $$\left( x ^ { 2 } - 7 x - 6 \right) \left( x ^ { 2 } + 9 x - 9 \right)$$

A) $x ^ { 4 } + 2 x ^ { 3 } - 15 x ^ { 2 } + 54 x + 9$
B) $x ^ { 4 } + 2 x ^ { 3 } - 78 x ^ { 2 } + 9 x + 54$
C) $x ^ { 4 } - 2 x ^ { 3 } - 72 x ^ { 2 } + 9 x + 54$
D) $x ^ { 4 } + 2 x ^ { 3 } - 78 x ^ { 2 } + 9 x - 54$
E) $x ^ { 4 } + 2 x ^ { 3 } - 78 x ^ { 2 } + 63 x + 54$

Question 76

Find the product. $6 ( 3 t + 5 ) ( t - 4 )$

A) $9 t ^ { 2 } - 2 t - 15$
B) $3 t ^ { 2 } - 7 t - 20$ $9 t ^ { 2 } - 2 t - 15$
C) $18 t ^ { 2 } + 42 t - 120$
D) $18 t ^ { 2 } - 42 t + 120$
E) $18 t ^ { 2 } - 42 t - 120$

Question 77

Find the product. $( 8 z + 1 ) ( 8 z - 1 )$

A) $64 z ^ { 2 } - 1$
B) $64 z ^ { 2 } - 16 z - 1$
C) $64 z ^ { 2 } + 1$
D) $16 z ^ { 2 } - 1$
E) $16 z ^ { 2 } + 1$

Question 78

Find the product. $\left( 5 b ^ { 5 } \right) \left( 3 b ^ { 6 } \right)$

A) $15 b ^ { 11 }$
B) $15 b ^ { 30 }$
C) $8 b ^ { 11 }$
D) $8 b ^ { 30 }$
E)none of these

Question 79

Solve the equation. $( t - 38 ) ^ { 2 }$ = $( t + 38 ) ^ { 2 }$

A)1
B)0
C)38
D)-38

Question 80

Find the product. $$( 4 a - 4 t ) ^ { 2 }$$

A) $16 a ^ { 2 } - 4 a - 4 t + 16 t ^ { 2 }$
B) $16 a ^ { 2 } - 16 t ^ { 2 }$
C) $16 a ^ { 2 } + 16 t ^ { 2 }$
D) $16 a ^ { 2 } - 32 a t + 16 t ^ { 2 }$
E) $16 a ^ { 2 } - 16 a t + 16 t ^ { 2 }$