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## Algebra (all content)

### Course: Algebra (all content)ย >ย Unit 1

Lesson 5: Writing algebraic expressions introduction- Writing basic expressions with variables
- Writing basic expressions with variables
- Writing basic expressions with variables
- Writing expressions with variables
- Writing expressions with variables
- Writing expressions with variables & parentheses
- Writing expressions

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# Writing expressions with variables & parentheses

Learn how to write algebraic expressions that involve grouping quantities in parentheses. 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?(11 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.(4 votes)

- at2:23Salman says 4+(2*(7-2x)). Can't he just say 4+2(7-2x)?(18 votes)
- according to the PEMDAS order of operations,both will work :)(1 vote)

- How would you write half of 14 in an algebraic expression(5 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)(3 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?(2 votes)
- well, 34+ 32x is in simplest form, because you don't know the value of x.(8 votes)

- How would 7+ -2x be the same as 7- 2x ?(3 votes)
- For the last question, couldn't we have written the answer in this way 4+2(7-2x)?(1 vote)
- 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.(3 votes)

- how does 7+-2x==7-2x,how do we drop the + sign?(1 vote)
- 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(2 votes)

- How do you type the dot symbol for multiplication?(1 vote)
- On the keyboard, we use the * (shift-8 key) in place of the dot for multiplication.(3 votes)

- how do we do it if the letter is not x. Example: 12 more than 8.2 times a number n(1 vote)
- 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 .(1 vote)

- couldn't you also expand 8(-5+4x)+6 and make it -34 + 32x?(2 votes)
- Yes it's true that 8(-5+4x)+6 simplifies to -34+32x, because 8(-5+4x)+6 = -40+32x+6 = -34+32x.

The expression in the lesson was actually -8(-5+4x)+6, which would simplify to 46-32x because -8(-5+4x)+6 = 40-32x+6 = 46-32x.

I believe that the skill being taught in the lesson is just translating English words to algebraic expressions without simplifying, but yes, simplifying algebraic expressions is also an important skill.(1 vote)

## 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.