# Lesson: Expanding Expressions

## Comment on Expanding Expressions

### ab < 0

ab < 0
bc > 0

QUANTITY A: ac
QUANTITY B: 0

GIVEN: ab is NEGATIVE and bc is POSITIVE

So, (ab)(bc) = (NEGATIVE)(POSITIVE) = NEGATIVE
Simplify left side to get: ab²c = NEGATIVE
Rewrite as: (ac)(b²) = NEGATIVE
Since b² must be positive, we can write: (ac)(POSITIVE) = NEGATIVE
This tells us that ac must be NEGATIVE

So, we get:
QUANTITY A: NEGATIVE
QUANTITY B: 0

0 is greater than a NEGATIVE number

Cheers,
Brent

Crazily, I saw this whole algebraic thing as two relationships, in which (A) is the toxic union of two people, a and b. It is toxic because their result value is less than zero (<0), so one of them two is the toxic potentiator. Then I see that b conjoined with c and had a positive result (>0), so a is the one that messes things up, and makes the end result negative. In a relationship of a and c nothing good can come out of it since it's got a included, so the result will be negative as well, being less than zero. Crazy, but it worked for my abstract mind. Advice: Stay away from a. Ha! Great reasoning!

Cheers,
Brent

### At 7:07, is that a typo?

At 7:07, is that a typo? Wouldn't (5y^3) (4y^4) = 20y^7 and not 20x^7? ### Good catch - thanks!

Good catch - thanks!
I'll fix that shortly.

Cheers,
Brent

### Regarding the 2nd question

Regarding the 2nd question from the activities (https://greprepclub.com/forum/x-is-different-from-zero-9213.html). I like your approach better than what I did, but I want to know if what I did is allowed. So, I had 3x^2 vs 9x^2 and then subtracted 3x^2 from both sides. At that point I had 0 vs 6x^2. I reasoned that no matter what x is, x^2 will be positive, so 6 times a positive number will always be positive, so B is greater than A. So, B is the answer. That's perfectly sound reasoning.
Nice work!

Cheers,
Brent

### Hello Brent,

Hello Brent,
Please, can you explain a little more how did you get to know those values?

You mentioned the following in the solution:

"We already know that 72.42 = 72 + 42/100"

https://greprepclub.com/forum/gre-math-challenge-14-72-42-k-24-n-333.html
Thank you Let's do a few conversions from decimals to fractions:
0.5 = 5/10 (aka 1/2)
0.7 = 7/10
0.24 = 24/100 (aka 6/25)
0.86 = 86/100 (aka 43/50)
0.123 = 123/1000
0.811 = 811/1000
0.125 = 125/100 (aka 1/8)

So, we know that 0.42 = 42/100

Also, 72.42 = 72 + 0.42
= 72 + 42/100

Likewise, 13.549 = 13 + 0.549
= 13 + 549/100

For more on conversions from decimals to fractions, watch https://www.greenlighttestprep.com/module/gre-arithmetic/video/1066

Does that help?

Cheers,
Brent

### So In this case you assume

So In this case you assume that 72 is equal to 24K. And the rest is the decimal. Is there any other approach to solve this exercise that you may know?
Thank you 