Manipulating expressions using structure | Mathematics I | High School Math | Khan Academy

So we're told that suppose a plus b is equal to zero. Which of these expressions equal a * b? And like always, pause the video and see if you can figure it out. These are actually pretty fun problems!

All right, 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 * b equal to? So a * 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 * b would be negative b * b, which is equal to negative b².

Another option is I could... I could... I could instead of saying a is equal to b, I could say that b is equal to a if we multiplied both sides by 1. So b is equal to a, and so instead of substituting a, I could substitute b with a.

And so this expression would be a * a, which is equal to a². So let's see which of these choices are... There's a negative b², but not negative a². So we see the negative a² right over there. So I'm feeling good! I'm feeling good about that choice.