Which property justifies each step?
Problem A: (6 + 2)a + 8b
= 8a + 8b
Problem B: 8a^2 + (8a + a^2) + 7a
= 8a^2 + (a^2 + 8a) + 7a
Problem C: 8a^2 + (a^2 + 8a) + 7a
= (8a^2 + a^2) + 8a + 7a
Problem D: (6a + 2a) + 8b
= (6 + 2)a + 8b
Thanks!
Problem A: (6 + 2)a + 8b
= 8a + 8b
no property justifies the steps, since they are wrong
Problem B: 8a^2 + (8a + a^2) + 7a
= 8a^2 + (a^2 + 8a) + 7a
You didn't do anything!
= 8a^2 + a^2 + 8a + 7a
= 9a^2 + 15a , used the distributive property, then just added like terms
Problem C: 8a^2 + (a^2 + 8a) + 7a
= (8a^2 + a^2) + 8a + 7a
again, incorrect
= 8a^2 + a^2 + 8a + 7a
= 9a^2 + 15a
B and C are the same problem
Problem D: (6a + 2a) + 8b
= (6 + 2)a + 8b , you used the distributive property in reverse (common factoring)
= 8a + 8b
forget my response to A
you are correct
A has the right result, but does not name the property used.
C uses the associative property of addition
To justify each step in the given problems, we need to use several properties of arithmetic and algebra. Let's go through each problem:
Problem A: (6 + 2)a + 8b = 8a + 8b
In this problem, the distributive property is used to simplify the expression. The coefficient outside the parentheses (6 + 2) is distributed to both terms inside the parentheses, resulting in 6a + 2a. Then, the like terms (6a and 2a) are combined to get 8a.
Problem B: 8a^2 + (8a + a^2) + 7a = 8a^2 + (a^2 + 8a) + 7a
This problem uses the commutative property to rearrange the terms inside the parentheses. By changing the order of the terms (8a and a^2), we can group the like terms (8a and a^2) together. This does not change the overall value of the expression.
Problem C: 8a^2 + (a^2 + 8a) + 7a = (8a^2 + a^2) + 8a + 7a
In this problem, the associative property is used to regroup the terms inside the parentheses. By changing the grouping within the parentheses, we can rearrange the terms and still achieve the same result.
Problem D: (6a + 2a) + 8b = (6 + 2)a + 8b
This problem once again applies the distributive property. The sum of (6a + 2a) is simplified to 8a by combining the like terms. This leads to the final form, (6 + 2)a + 8b.
By using these properties of arithmetic and algebra, we are able to justify each step in the given problems.