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

less than 1m read

·Nov 11, 2024

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.

Jacksonian Democracy part 3

Meet the Ice Cook | Drugs, Inc.

View All

15 Ways You Always Sound Smart

Ever been to a family dinner and there’s that cousin that makes rocket science look like making pancakes? Or maybe you’re at a get-together and you find yourself talking to someone who oozes intelligence. Or you find your crush happens to be a chemistry m…

Tesla : The Ponzi Factor

When we think about the stock market, we think about money, the finance industry, businesses, and making money from investing in successful businesses. The belief is investing in successful businesses is what leads to investment profits, and there’s a dir…

Warren Buffett: 90 Years of Wisdom Summed up in 16 Minutes

And yeah, Ben Franklin did this and my old boss Ben Graham did this at early ages in their young teens. They just—Ben Graham looked around and he said, “Who do I admire?” You know, and he wanted to be admired himself. He said, “You know, why do I admire t…

Definite integrals intro | Accumulation and Riemann sums | AP Calculus AB | Khan Academy

What we’re going to do in this video is introduce ourselves to the notion of a definite integral. With indefinite integrals and derivatives, this is really one of the pillars of calculus. As we’ll see, they are all related, and we’ll see that more and mor…

Why Scorpions Glow in the Dark

Finding scorpions in the desert at night is surprisingly easy. All you need is an ultraviolet torch because scorpions are incredibly fluorescent. Fluorescence means their bodies absorb ultraviolet light and reradiate it in the visible part of the spectrum…

Startup Advisor Equity? - Pebble Watch Founder Eric Migicovsky

Bringing on advisors or creating a network of people who can help you is critical for an early stage founder, especially a first-time founder. I did it myself; I had ups and downs in the process, but that’s just like every other part of building a startup…

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

More Articles