algebra

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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)

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