Writing expressions with variables & parentheses
About this video
The video turns word descriptions into algebraic expressions step by step, using parentheses to keep a whole expression together. 'Negative 5 plus 4 times x' becomes -5 + 4x; multiplying it by -8 and adding 6 gives -8(-5 + 4x) + 6. Similarly, 'the sum of 7 and the product of -2 and x' is 7 - 2x, and 4 plus 2 times that expression is 4 + 2(7 - 2x).
You'll be able to
- write an expression from a word description, such as 'the product of -2 and x'.
- use parentheses to multiply a whole expression by a number.
- build a bigger expression step by step from a smaller one.
- recognise that 7 + -2x and 7 - 2x are the same expression.
Key words
- expression
- Numbers, variables and operations put together, like -5 + 4x.
- product
- The answer when you multiply; 'the product of -2 and x' is -2x.
- sum
- The answer when you add; 'the sum of 7 and 3' is 7 + 3.
- quantity
- A group that is treated as one thing, often shown in parentheses.
- parentheses
- Brackets ( ) that keep an expression together so an operation applies to all of it.
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.
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