Give the reason (property) for each step in the simplification.
8(a+b)-3a
(8a+8b)-3a
(8b+8a)-3a
8b+(8a-3a)
8b+5a
I think I figured out a few of them
the fist is given
second is distributive
third is Commutative
and I am not sure about the rest
associative
8a-3a = (8-3)a = 5a distributive again
To simplify the expression 8(a+b) - 3a, we will follow the order of operations (PEMDAS) and combine like terms.
Step 1: Distributive Property
The expression starts with 8(a+b). According to the distributive property, we need to multiply 8 by both a and b.
8 * a = 8a
8 * b = 8b
So, 8(a+b) becomes (8a+8b).
Step 2: Combine Like Terms
Now we have (8a+8b) - 3a. Here we need to combine the like terms, which means adding or subtracting a and 8a terms and b and 8b terms separately.
Sum of a terms: 8a - 3a = 5a
Sum of b terms: 8b
So, (8a+8b) - 3a simplifies to 8b + 5a.