Question

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!

Answer 1

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

Answer 2

forget my response to A
you are correct

Answer 3

A has the right result, but does not name the property used.
C uses the associative property of addition