im going to give and example: 7(b+3) would the answer be -8z?

Samantha,

Hi there! I am not sure where the -8z comes in, but I sure can help with the 7(b+3)!

First, we need to know the difference between an equation and an expression. Here is the easiest way. When you see an equal sign (=) in a problem, you know you have an equation. If there is no =, it is considered an expression. 7(b+3) is therefore an expression. If you had something like 7(b+3) = 0, then you would have an equation.

You can simplify an expression, but you cannot solve it. We can never know what b is equal to in 7(b+3), so it will always just be b. The only thing we can do here is remove the parentheses. To do so, we must distribute the 7 to each item in the parentheses. In other words, we are going to multiply everything in parentheses by a factor of 7. Thus, 7(b+3) would become 7*b + 7*3, and 7*3 would then multiply to become 21. Your final answer here would be 7b+21. Be careful here though! If you had something like 7(b-3), your answer would be 7b-21... see the difference? If you have an expression, the variable a.k.a. letter (in this case, b) will always be a part of your answer. Remember, you can't solve for b!

So what do we need to solve for b? An equation! Let's go back to our example of an equation, where 7(b+3)=0. Now we have a way to solve for b! You will still simplify as you did with your expression, so we will end up with 7b+21 = 0. To solve for b, we need everything with a b in it on one side of the equal sign, and everything else on the other side of the equal sign. Here, we need to get 7b on one side, and put the 21 on the other side. How do we get rid of the 21? We subtract from BOTH SIDES of the equal sign. This means we will have 7b + 21 - 21 = 0 - 21. The most important lesson here is that what we do to one side of the equation, we must do to the other (this is why we subtract 21 from the right side!). This will leave us with 7b = -21. Now that we have b all to itself, we need to get rid of that 7, but how? Divide BOTH SIDES by 7! This means we will have (7b)/7 = -21/7. Remember, any number divided by itself equals 1, leaving us with b = -21/7, and -21 divided by 7 equals -3. Your final answer is b=-3. If you have an equation, you can solve it to find the identity of your variable/letter. 

Sorry it was a long explanation... just wanted to be as thorough as possible. 

Another helpful hint: when you have either an equation or an expression, the variable stays the same throughout. You cannot change letters (another letter might have a different value). So if you start a problem with b, you will never change the b to z... it will always stay b! :]

7(b + 3)

This is an expression. You will distribute the 7 but you cannot combine the term, so you are basically writing the expression another way, but there is no solution. You will not find the value of b. The problem does not require it. You are just asked to show the distributive property over addition. Therefore 

7x b + 7 x 3 is all you can do. To simplify

7x b is 7b and 7 x 3 is 21

hence the answer is

7b + 21 

This is a distribution problem.  Think of the 7 as something that will effect both things inside the parentheses.  7 (b + 3) = 7 times b plus 7 times 3    or     7b+21

Distribution can also happen when the parentheses come first; as in (3 - x) 4 = 12- 4x

And remember to pay close attention to the signs; positive or negative.  Multiplying two numbers whose signs that are the same will result in a positive number so:

8(4 + 3) = 8(4) + 8(3) = 32 + 24 = 56 

and

-8 (- 4 ) = -8 (-4) = 32

whereas multiplying 2 numbers that have opposite signs will always result in a negative number so,

3 (-6) = -18   and -3 (6) = -18

If you need help with distribution it is important to get that help very early in school. That makes algebra much easier.

There is no z in the equation you used as an example so that would not be the answer. With this kind of problem you will use the distributive property and 7 will be multiplied by everything in the parenthesis as such 

7(b+3)=7b+21 I hope this helps you