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)
Problem A:
e1. = 6a + (2a + 8b) (Asymmetric)
f2. = (6a + 2a) + 8b (Associative)
b3. = (6 + 2)a + 8b (Substitution)
c4. = 8a + 8b (Associative)
Problem B:
c5. = 8a^2 + (a^2 + 8a) + 7a (Commutative)
b6. = (8a^2 + a^2) + 8a + 7a (Associative)
For numbers 7 – 12, Combine like terms:
c7. 9y^2 + 13y^2 + 3 = 22y^2 + 3
a8. 12a^2 + 14a - 11a^2 = a^2 + 14a
d9. 14a^2 + 27 + 13a^2 = 27a^2 + 27
d10. 5a + 10b + 7 + 5b = 5a + 15b + 7
c11. 3(x + 2y) - 2y = 3x + 4y
b12. 5x + 3(x - y) = 8x - 3y
f13. Seven times a number, added to the sum of the number and eight = 7n + (n + 8)
a14. A number multiplied by -7, subtracted from the sum of 11 and three times the number = 11 + 3n - 7n
e15. A number multiplied by 9, added to -8, subtracted from 5 times the number = 5n - 9 + (-8)
a16. 2 times a number added to -7, added to 6 times the sum of 3 times the number and 8 = 2n - 7 + 6(3n + 8)
e17. Seven times a number added to 7 subtracted from triple the sum of six times the number and 7 = 3(6n + 7) - (7n + 7)
Problem A: 6a + (8b + 2a)
To simplify this expression, we need to combine like terms. Like terms are terms that have the same variable and exponent.
In this expression, we have two terms with variable "a" and one term with variable "b".
Step 1: Combine the terms with "a".
We have 6a and 2a. Since they have the same variable "a", we can add their coefficients. 6a + 2a = 8a.
Step 2: Combine the terms with "b".
We have 8b. There are no other terms with variable "b", so we leave it as it is.
Final simplified expression: 8a + 8b
Explanation: To combine like terms, we add the coefficients of the terms with the same variable.