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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?(36 votes)
- 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.(25 votes)

- How does -bxb= -b^2?

-b^2 = a positive where as -bxb = a negative, no?(16 votes)- -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.(27 votes)

- 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.(6 votes)
- 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(12 votes)

- 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 ?(3 votes)
- 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.(4 votes)

- Suppose a+b=0, which is equal to a-b. what is the expression(2 votes)
- Hi. Can you elaborate? How can a+b = 0 be equal to a-b?(2 votes)

- How is -b times b the same as -b squared?....the latter would be a positive number right?(0 votes)
- 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(6 votes)

- How would you solve this equation:

x square plus y square = 28

xy = 14

Therefore what is x square minus y square

KINDLY HELP!(2 votes) - 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(3 votes)

- 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?(2 votes) - 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?(2 votes)
- 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.(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.