a[2+b(2+c)]=

Question

descriptive property simplify each expression

Answer 1

(Did you mean the distributive property?) :)

Use the order of operations: Parentheses Exponents Multiplication Division Addition Subtraction

 

a[2+b(2+c)]

 

1. The brackets are considered parentheses so we do that 1st. In the brackets is another set of parentheses so look at those first before solving the brackets as a whole. We can't add 2+c so we disregard solving what is in the parentheses. Looking at the whole bracket we have addition (a+..) and multiplication (b(2+c). Multiplication comes before addition in the order of operations, so we do that first.  (distribute the b to every term in the parentheses)

 

a[2+ (b*2) + (b*c)]   --> a[2+2b+bc]

 

2. Then we see if we can add anything in the brackets. We can't in this case because we have no like terms. For terms to be similar they have to have the exact same variables in each term. These have some of the same variables, but not exactly the same variables.

 

3. The only thing we can do now is multiply (distribute) the "a" outside the brackets (which we treat as parentheses) to everything inside the brackets

 

(a*2)+(a*2b)+(a*bc) --> 2a + 2ab + abc

 

4. Again, we see if we can add. We can't for the same reason listed in step 2. So this is our final answer.

 

2a + 2ab + abc

Answer 2

PEMDAS. That is what we have to remember.

 

a(2+b(2+c))

 

First, let us do the inside parentheses b(2+c); we get (2b + bc) which gives us a(2+(2b+bc)).

Next, let us distribute the "a"; we get (2a+2ab+abc)

 

Thus our final answer is:

 

2a + 2ab + abc