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Manipulating expressions using structure

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About this video

Given a + b = 0, Sal finds which expression equals a times b. He rearranges to a = -b (or b = -a) and substitutes to show ab = -b^2 = -a^2, then picks -a^2 from the choices.

You'll be able to

  • rearrange an equation like a + b = 0 to express one variable in terms of the other.
  • substitute to rewrite a product such as ab.
  • recognise equivalent expressions like -a^2 and -b^2 when a = -b.

Key words

substitute
Replace a variable with something equal to it, like replacing a with -b.
expression
A maths phrase with numbers, variables and operations but no equals sign, like -a^2.
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.

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