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Problem A: 6a + (8b + 2a)

e1. = 6a + (2a + 8b)

Asymmetric

Bdistributive

Cmultiplicative identity

Dcommutative

Ereflexive

Fsubstitution

f2. = (6a + 2a) +8b

Adistributive

Bassociative

Csubstitution

Dmultiplicative property of zero

Emultiplicative identity

Fadditive identity

b3. = (6 + 2)a + 8b

Areflexive

Bassociative

Csubstitution

Dcommutative

Etransitive

Fdistributive

c4. = 8a + 8b

Aassociative

Breflexive

Cadditive identity

Dcommutative

Esubstitution

Fsymmetric

Problem B: 8a^2 + (8a+a^2) + 7a

c5. = 8a^2 + (a^2 + 8a) + 7a

Acommutative

Btransitive

Cassociative

Dreflexive

Esymmetric

Fmultiplicative property of zero

b6. = (8a^2 + a^2) + 8a + 7a

Asymmetric

Bcommutative

Creflexive

Ddistributive

Emultiplicative identity

Fassociative

For numbers 7 – 12, Combine like terms

c7. 9y^2 + 13y^2 + 3

A22y^2 + 3

By

C 22y^4

D25y

E25y^2

F22y

a8. 12a^2 + 14a - 11a^2

A37a^5

Ba^2 + 14a

C22a^3

D11a^2

E11a

F33a^3

d9. 14a^2 + 27 + 13a^2

A54a

B27a^2

C54a^2

D27a^2 + 27

E27(a + 1)

F27a^5

d10. 5a + 10b + 7 + 5b

A5a + 15b^2 + 7

B20ab + 7

C15ab + 12b

D5a + 15b + 7

E10ab^2 + 7

F27ab^2

c11. 3(x + 2y) - 2y

A3x

B3x + 8y

C3x + 4y

Dx^3 + 6y^3

Ex^3

F3x + y

b12. 5x + 3(x - y)

A5x^2 + 3x - 3y

B8x - 3y

C15x^2 - 3y

D2x - 3y

E2x - y

F5x^4 - y^4

Write the phrase as a mathematical expression. Use x to represent the number. Combine like terms if possible.

f13. Seven times a number, added to the sum of the number and eight.

A7 + n + 8

B7 – n + 8

C56n

D7 + 8n

E7n + (n + 8)

F(7n) + (8n)

a14. A number multiplied by -7, subtracted from the sum of 11 and three times the number

A-7n – (11 + 3n)

B(-7 – 11) -3 n

C11 - 7n

D(11 + 3n) - (-7n)

E3n(7 - -11)

F(11 – 3n) - (-7n)

e15. A number multiplied by 9, added to -8, subtracted from 5 times the number

A9n + 8 - 5(5n)

B5n – 9+ 8

C9n + 8 – 5n

D 5n – 9 + (-8)

E5n – [9n + (-8)]

F5n – 9n + 8

a16. 2 times a number added to -7, added to 6 times the sum of 3 times the number and 8

A2n + (-7) + 6(3n + 8)

B2n + 7 – 6 + 3n +8

C2 + (-7) + 6 + 3n (8)

D2n + (-7) + 6 + 3n + 8

E(6)3n + 8(2n) + (-7)

F-7 = 6(2n + 3n) + 8

e17. Seven times a number added to 7 subtracted from triple the sum of six times the number and 7

A7n + 3+ 6n - 7

B7n + 6n + 7(3)

C6n + 7 – 7n + 7

D(7n + 7) – 3(6n + 7)

E7n + 7 – 3(6n + 7)

F3(6n + 7) – (7n + 7)