Main content

### Course: Algebra basics > Unit 2

Lesson 3: Writing algebraic expressions# Writing expressions with variables & parentheses

In this math lesson, we learned about expressions and how to simplify them step by step. We explored adding and multiplying expressions, like negative numbers and variables. By practicing these skills, we can solve more complex algebra problems with ease and confidence. Created by Sal Khan.

## Want to join the conversation?

- in the first problem why did he know to multiply -5+4x from the word product?(14 votes)
- Hi Valentina, I know it's late but i will answer in case if anyone has the same question. Sal knew because product/times stands for multiplication. Let's consider I have a expression 2 + 5, the product of 4 and that expression means 4*(2 + 5). Other more simple example could be, the product of 2 and 5 means 2 * 5 which is the same as saying 2 times 5. Hope it helps.(6 votes)

- at2:23Salman says 4+(2*(7-2x)). Can't he just say 4+2(7-2x)?(24 votes)
- according to the PEMDAS order of operations,both will work :)(6 votes)

- Would it be better, instead of 4+(2·(7-2x)), to answer with 4+2·(7-2x) or, even better yet, 4+2(7-2x)? It seems that the extraneous parenthesis in the video answer might get marked wrong in many classrooms.(8 votes)
- Hi Dale! Yes, technically it would be a bit easier to remove the parenthesis in the case of the Order of Operations, but for some people who get confused, it's better to have a reminder to do the things in parenthesis first. Hope this clears up any problems!(10 votes)

- When you got the answer for the first question,shouldn't the answer be simplifies further to -34+32x? Why did you just leave it like that without simplifying. Wouldn't you get points off on a test or quiz grade?(6 votes)
- well, 34+ 32x is in simplest form, because you don't know the value of x.(11 votes)

- how does 7+-2x==7-2x,how do we drop the + sign?(6 votes)
- Adding anegative number has the same effect as subtracting the number i.e. in basic arithmetic 4+(-7)=-3 and 4-7=-3

Watch this video https://www.khanacademy.org/math/arithmetic/arith-review-negative-numbers/arith-review-add-negatives-intro/v/adding-negative-numbers(9 votes)

- How would you write half of 14 in an algebraic expression(8 votes)
- To write anything as a fraction of itself (e.g. half of 14, one third of 6, e.t.c) , you will just need to multiply the number you're dividing by the numerator (e.g. half of 14 = 1/2*14=14/2=7)(7 votes)

- How would 7+ -2x be the same as 7- 2x ?(6 votes)
- I'm confused about when it says quantity. I think it just means to solve the problem or is there another definition?(6 votes)
- "The quantity of 4 times x" just means 4x. This wording is used because the value of x is currently unknown.(2 votes)

- For the last question, couldn't we have written the answer in this way 4+2(7-2x)?(3 votes)
- The main reason that the parentheses were added is because of the word "quantity" which is an indication of grouping a set of terms together. You are correct that the parentheses are not needed and would do nothing if we expand this.(5 votes)

- how do we do it if the letter is not x. Example: 12 more than 8.2 times a number n(3 votes)
- It is the same procedure. But one change will make it different. Substitute n as x and follow the same steps you would usually do. Then, replace x as n and submit the answer.

P.S The answer to your example is 12 + 8.2n .(3 votes)

## Video transcript

First consider the
expression for negative 5 plus the quantity of 4 times x. Now, take the product of
negative 8 and that expression and then add 6. So let's do it step by step. First, we're going to have
this expression-- negative 5 plus something. So it's going to be negative 5
plus the quantity of 4 times x. Well, that's just
going to be 4x. So it's going to be
negative 5 plus 4x. So that's this
expression up here. Now, take the product
of negative 8, so were going to
just take negative 8, and we're going to multiply
the product of negative 8 and that expression. So we're going to
take negative 8 and multiply it
so that expression is this thing right over here. So if we say the product of
negative 8 in that expression is going to be negative
8 times that expression, that expression is negative 5
plus 4x, so that's negative 8. That's that expression. The product of the two, so
we could put a multiplication sign there, or we could
just leave that out and implicitly it would
mean multiplication, take the product of negative
8 and that expression and then add 6. So that would be then
adding 6 right over here. So we could write it as negative
8 open parentheses negative 5 plus 4x and then add 6. Let's do one more. First, consider the expression
the sum of 7 and-- so that's going to be
7 plus something-- and the product of
negative 2 and x. The product of negative
2 and x is negative 2x. So it's 7 plus negative 2x. We could write
that as 7 minus 2x. So this is equal to 7 minus 2x. These are the same expression. What expression would be 4 plus? So now we're saying
4 plus the quantity of 2 times that expression? So it's going to be
4 plus some quantity. I'll put that in parentheses. The quantity of 2
times-- I'll do this in magenta or in yellow. 2 times that expression--
let me do this in blue-- that expression is this
thing right over here. So 4 plus the quantity of 2
times that expression, 2 times 7 minus 2x. And we are done.