# Question: Products of Binomials

## Comment on Products of Binomials

### For this question when you

For this question when you get to -2xy for quant A and -23xy for quant B couldn't you add 2xy to both sides and make quant A equate to 0 and quant B equate to -21xy. then dividing by -21 would cause quant A to remain 0 and Quant B to become xy. Shouldn't that make the answer D?

### Be careful. You must not

Be careful. You must not divide both quantities by a negative values (for more on this, see https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...)

### Once you have -2xy and -23xy,

Once you have -2xy and -23xy, isn't it possible to assume that Quant B will always be larger ... since the xy will come out negative (and an equal value) on both sides; then, once multiplied by -23 on the QB side will always be larger than multiplying it by -2 on the QA side.

### Yes, that's a perfectly valid

Yes, that's a perfectly valid approach.

However, that kind of mental manipulation might be hard for some people, in which case we can still reach the same conclusion by performing the steps outlined in the video.

### Thanks – these videos are

Thanks – these videos are great, you're a fabulous help.

I solved the quadratic equations on both sides by supposing x =-1 and y=1 for which Quantity A's result was 5 and Quantity B was 25. thus I reached the conclusion that Quantity B was greater. The answer was B.
Kindl let me know this technique will be most beneficial for a question such as the one being discussed or should I follow your method to the last dot because I frankly find it confusing.

### When you say that you "solved

When you say that you "solved" the quadratic equations, what do you mean? I ask because neither quantity is an equation (no equals sign).

It sounds like you just plugged x =-1 and y=1 into both quantities and found that Quantity B was greater. This is a good START. However, if you use the Plugging In Numbers approach, you can't just stop at plugging in one value, since there might be other values of x and y such that the two quantities are equal or Quantity A is greater (for more on this, watch the part that starts at 2:50 of this video: https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...)

Of course, with this question, it turns out that the correct answer is B, but we can't make this conclusion with absolute certainty by plugging in only one set of numbers.

### How am I supposed to know

How am I supposed to know that I have to add 23xy on both sides instead of adding 2xy on both sides?

### We could have done that as

We could have done that as well. It would look something like this:

QUANTITY A: -2xy
QUANTITY B: -23xy

Add 2xy to both quantities to get:
QUANTITY A: 0
QUANTITY B: -21xy

ASIDE: Notice that approach makes things a LITTLE more cumbersome, since we now have to deal with a NEGATIVE expression. That said, we can keep going.

QUANTITY B equals -21xy
We can also say that QUANTITY B equals (NEGATIVE)(x)(y)

Since we're told that x is NEGATIVE and y is POSITIVE, we can now say that:
QUANTITY B equals (NEGATIVE)(NEGATIVE)(POSITIVE)

This means that QUANTITY B equals some POSITIVE number, which means QUANTITY B must be greater.

Does that help?

Cheers,
Brent

### Aside: Notice that we have

Aside: Notice that we have more than one option here. The key rule is that we must perform the same operation to each quantity. And we must not divide or multiply both quantities by a negative value.

Given this, here's yet another approach:

QUANTITY A: -2xy
QUANTITY B: -23xy

Add 2xy to both quantities to get:
QUANTITY A: 0
QUANTITY B: -21xy

Add 21xy to both quantities to get:
QUANTITY A: 21xy
QUANTITY B: 0

Divide both quantities by 21 to get:
QUANTITY A: xy
QUANTITY B: 0

Since we're told that x is NEGATIVE and y is POSITIVE, we can know that:
QUANTITY A evaluates to be some NEGATIVE value, which means QUANTITY B must be greater.

### I simplified both sides to

I simplified both sides to get '-2xy' and '-23xy'. Here, can I cancel the negative signs on both sides to get '2xy' and '23xy'?

### No, you can't make that step,

No, you can't make that step, because in order to "cancel the negative signs on both sides" what you're really doing is multiplying both sides by -1, which is not allowed.

Consider this example:
QUANTITY A: -1
QUANTITY B: -10
Here, Quantity A is greater than Quantity B

If we multiply both sides by -1, we get:
QUANTITY A: 1
QUANTITY B: 10
Now Quantity B is greater than Quantity A

For more on this, watch: https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...

Cheers,
Brent

### -2xy and -23xy

-2xy and -23xy

At this point is it reasonable to say xy will be a negative value and multiplying it by a negative produces a + value. 23 times the same product is bigger than 2 times.

### That's a perfectly reasoned

That's a perfectly-sound strategy - nice work!