Video Transcripts: Writing Algebraic Expressions

Writing basic expressions with variables 

Let's do some examples of the writing expressions with variables exercise. So it says "Write an  expression to represent 11 more than a." Well you could just have a but if you want 11 more  than a, you would wanna add 11 so you could write that as a plus 11. You could also write that as 11 plus a. Both of them would be 11 more than a. So let's check our answer here. We got it right. Let's do a few more of these. "Write an expression to represent the sum of d and 9." So the sum of d and 9, that means you're gonna add d and 9. So I could write that as d plus 9 or I could  write that as 9 plus d. And check our answer. Got that right. Let's do a few more of these.  "Write an expression to represent j minus 15." Well, I could just write it with math symbols  instead of writing the word minus. Instead of writing M-I-N-U-S, I could write j minus 15. And  then I check my answer. Got it right. Let's do a few more of these. This is a lot of fun. "Write an  expression to represent 7 times r." There's a couple ways I could do it. I could use this little dot  right over here, do 7 times r like that. That would be correct. I could literally just write 7r. If I just  wrote 7r that would also count. Let me check my answer. That's right. Let me do a couple of  other of these just so you can see that I could've just done 10 and this is not a decimal, it sits a  little bit higher than a decimal. It's multiplication and the reason why once you start doing  algebra, you use this symbol instead of that kind of cross for multiplication is that x-looking  thing gets confused with x when you're using x as a variable so that's why this is a lot more  useful. So we wanna write 10 times u, 10 times u, let's check our answer. We got it right. Let's  do one more. "Write an expression to represent 8 divided by d." So we could write it as 8 and  then I could write a slash like that, 8 divided by d. And there you go. This is 8 divided by d. Let  me check, let me check the answer. I'll do one more of these. Oh, it's 6 divided by b. Alright,  same thing. So 6, I could use this tool right over here. It does the same thing as if I were to press the backslash. So 6 divided by b. Check my answer. We got it right. 

Writing expressions with variables 

What I want to do in this video is write the algebraic expressions that represent the same thing  that these statements are saying. So this first statement, they say the sum of negative 7 and  the quantity 8 times x. So the sum-- so we're going to have an addition here-- of negative 7 and  the quantity 8 times x. So the quantity 8 times x, well, that's just 8x. So I can just write 8x over  there. So it is negative 7 plus 8x. Or you could view this as the sum of negative 7 and the  quantity 8 times x. Let's do the next one. Take the quantity negative 3 times x and then add 1.  So the quantity negative 3 times x, we can write that as negative 3x. And then we need to add 1  to that. So that's going to be plus 1. Now this one. Negative 6 plus-- so we can write negative 6  plus something-- the product of negative 1 and x. So the product of negative 1 and x, that's just  going to be negative 1x, which is the same thing as negative x. So we can write this as negative  6 plus negative x. Or we can just write this-- this is the exact same thing as negative 6 minus x.  And we are done. 

Writing expressions with variables & parentheses 

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.