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?

Why does b^2 has to be negative to be the correct answer? Isn't b^2 == (-b)^2?

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

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

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Course: Mathematics I (2018 edition) > Unit 6

Lesson 5: Manipulating expressions with unknown variables

Manipulating expressions using structure

Name: Manipulating expressions using structure
Uploaded: 2016-02-15T12:20:14Z
Description: Given that a+b=0, Sal finds an expression equivalent to a*b.

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

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d n
Posted 8 years ago. Direct link to d n's post “Is it not also correct th...”
Is it not also correct that if a=0 and b=0 then ab equals 0?
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(36 votes)
Answer
- ＫＥＶＩＮ
  Posted 8 years ago. Direct link to ＫＥＶＩＮ's post “You've made a good observ...”
  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.
  Comment on ＫＥＶＩＮ's post “You've made a good observ...”
  (24 votes)
jack cameron
Posted 8 years ago. Direct link to jack cameron's post “How does -bxb= -b^2? -b^2...”
How does -bxb= -b^2?
-b^2 = a positive where as -bxb = a negative, no?
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(16 votes)
Answer
- Vu
  Posted 8 years ago. Direct link to Vu's post “-b² means -(b²). You take...”
  -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.
  Comment on Vu's post “-b² means -(b²). You take...”
  (27 votes)
Michael Folk
Posted 8 years ago. Direct link to Michael Folk's post “I dont get how -b^2 is eq...”
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.
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(6 votes)
Answer
- Vu
  Posted 8 years ago. Direct link to Vu's post “You weren't paying attent...”
  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
  Comment on Vu's post “You weren't paying attent...”
  (12 votes)
Arthur
Posted 7 years ago. Direct link to Arthur's post “I'm having trouble unders...”
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 ?
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(3 votes)
Answer
- Johnathan
  Posted 7 years ago. Direct link to Johnathan's post “WIth a + b equals 0, it's...”
  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.
  Comment on Johnathan's post “WIth a + b equals 0, it's...”
  (4 votes)
Rio Antonio Loya
Posted 6 years ago. Direct link to Rio Antonio Loya's post “Suppose a+b=0, which is ...”
Suppose a+b=0, which is equal to a-b. what is the expression
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(2 votes)
Answer
- Gard
  Posted 6 years ago. Direct link to Gard's post “Hi. Can you elaborate? Ho...”
  Hi. Can you elaborate? How can a+b = 0 be equal to a-b?
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  (2 votes)
mwesolo87
Posted 7 years ago. Direct link to mwesolo87's post “How is -b times b the sam...”
How is -b times b the same as -b squared?....the latter would be a positive number right?
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(0 votes)
Answer
- David Severin
  Posted 7 years ago. Direct link to David Severin's post “There is an issue of how ...”
  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
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  (6 votes)
jotinray
Posted 7 years ago. Direct link to jotinray's post “How would you solve this ...”
How would you solve this equation:
x square plus y square = 28
xy = 14
Therefore what is x square minus y square
KINDLY HELP!
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(2 votes)
Answer
Emad Omar
Posted 7 years ago. Direct link to Emad Omar's post “Why does b^2 has to be ne...”
Why does b^2 has to be negative to be the correct answer? Isn't b^2 == (-b)^2?
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(1 vote)
Answer
- David Severin
  Posted 7 years ago. Direct link to David Severin's post “While what you say is tru...”
  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
  Comment on David Severin's post “While what you say is tru...”
  (3 votes)
Kon Lon
Posted 7 years ago. Direct link to Kon Lon's post “Hello! How does one solv...”
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?
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(2 votes)
Answer
Waleed Sharkawy
Posted 7 years ago. Direct link to Waleed Sharkawy's post “how can I determine in ex...”
how can I determine in expression -a^2 we will remove the negative or no? Is a symbol means a number and we don't care about the sign so a maybe -1 or 1?
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(2 votes)
Answer
- David Severin
  Posted 7 years ago. Direct link to David Severin's post “You have to keep your neg...”
  You have to keep your negatives. If you look at the graphs of positive and negative coefficients for quadratics, positive coefficients have the parabola opening up, and negative coefficients have the graph opening down. IT may not affect the two x intercepts, but it will affect the range of the function, the y intercept, and if you have a maximum or minimum.
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  (1 vote)

Video transcript

- [Voiceover] So, we're sold that suppose a plus b is equal to zero. Which of these expressions equal a times b? And like always, pause the video, and see if you can figure it out. These are actually pretty fun problems. Alright, so, let's see if we can do a little bit of manipulation. So, we're told that a plus b is equal to zero. So, if we subtract b from both sides, we would get. So, if I subtract b from both sides, I would get a is equal to negative b. So, what is a time b equal to? So, a times b. Well, I could write this a few ways. I could substitute the a with a negative b, since we know a is equal to negative b. In which case, a times b would be negative b times b, which is equal to negative b squared. Another option is I could instead of saying a is equal to negative b, I could say that b is equal to negative a if we multiply both sides times negative one. So, b is equal to negative a. And so, instead of substituting a, I could substitute b with negative a. And so, this expression would be a times negative a, a times negative a, which is equal to negative a squared. So, let's see, which of these choices are there? There's a b squared, by not negative b squared. So, we see the negative a squared right over there. So, I'm feeling good. I'm feeling good about that choice.