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### Course: Algebra (all content)>Unit 5

Lesson 5: Manipulating expressions with unknown variables

# Manipulating expressions using structure

Given that a+b=0, Sal finds an expression equivalent to a*b.

## Want to join the conversation?

• Is it not also correct that if a=0 and b=0 then ab equals 0?
• You've made a good observation. If a = 0 and b = 0, then ab would indeed be equal to zero. I think within the context of the example, we are supposed to solve for either a or b with the assumption that a and/or b are not equal to zero. But as 0 is given as a choice it perhaps should have been included as a possible correct answer. You could try reporting it in the Tips section, or when you do the exercises and see this particular problem, you could report it then.
• How does -bxb= -b^2?
-b^2 = a positive where as -bxb = a negative, no?
• -b² means -(b²). You take the square then apply the negative sign, which is negative. If it was (-b)² then it would become positive.
• I dont get how -b^2 is equal to a - b....how do they come to that conclusion? I can substitute any number into -b^2 and it will not equal zero because -2*-2 does not equal zero for example. Its a stupid question imo.
• You weren't paying attention to the video.
The condition was a + b = 0 (with the assumption a and b are non-zeros). For this condition a*b=-a² or -b²
Let me use a numerical example.
if a = 2 then b=-2
a+b =0 or 2+(-2)=0
a*b = 2*(-2)=-4
-a²= -2²=-4
-b²= -(-2)²=-4
• I'm having trouble understing how this works, I get how to do, (a+b+c) (x+y) problems but these a+b equals things, can someone help me ?
• WIth a + b equals 0, it's simple to know that b has to be negative a (-a) so that a - a = 0. Then when it asks what is ab, then a * -a would be -a^2 because it's repetitive multiplication with a negative.

Hope this helps. Feel free to comment if you have any more questions.
• Suppose a+b=0, which is equal to a-b. what is the expression
• Hi. Can you elaborate? How can a+b = 0 be equal to a-b?
• How is -b times b the same as -b squared?....the latter would be a positive number right?
• There is an issue of how you write it that really makes a difference and as you later get to use the quadratic formula, it will make a difference
-b • b = - b^2 negative b squared (negative times a positive)
- b^2 is what it says it is negative b squared (square b and negate it)
(- b) ^2 = b^2 positive b squared (negative times a negative)
It all depends on how it is written
• How would you solve this equation:
x square plus y square = 28
xy = 14
Therefore what is x square minus y square
KINDLY HELP!
• Why does b^2 has to be negative to be the correct answer? Isn't b^2 == (-b)^2?
(1 vote)
• While what you say is true, b^2 is not equal to -b^2. You have no reason to put it In parentheses because he multiplied -b • b, not -b • -b like you are trying to argue
• Hello!

How does one solve this problem? I couldn't do it. I'd really appreciate if someone solved this problem.

if a+c/b = 3/2 and b/c = 3/4

then what is a/b?