# Lesson: FOIL Method for Expanding

## Comment on FOIL Method for Expanding

### 12-2sqrt35 isn't 10sqrt35

12-2sqrt35 isn't 10sqrt35 right?

### You're right, 12 - 2√35 does

You're right, 12 - 2√35 does not equal 10√35

However, we can say that 12√35 - 2√35 = 10√35

For more on this, watch: https://www.greenlighttestprep.com/module/gre-powers-and-roots/video/1042

Cheers,
Brent

### HI Brent,

HI Brent,
Question on this one (1st reinforcement)
https://gre.myprepclub.com/forum/which-is-greater-x-2-2-or-x-12433.html

On your 3rd step, if you divided both sides by x wouldn't you get -4 and 4, making the answer B?

The problem with that strategy is that we don't know whether x is positive, negative or zero.
In order to divide both quantities by a variable, we must be certain that the variable is POSITIVE.

For more on this, see https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi... (starting at 2:40 in the video.

Cheers,
Brent

### hi brent,

hi brent,
for sorry the first reinforcement activity: Is it true that since there are an infinite number of values for x, there is also an infinite number of solutions for both expressions, since no restrictions have been placed on x? will this be true for all expressions where no restrictions exist on the variable? does it follow that all comparison questions involving two expressions without restrictions are D?

Great question (and observation)!

That would be very helpful if we could say that, when comparing two expressions where each expression has infinitely many values, the correct answer will always be D. However, this won't always be the case.

Consider, for example, this question:
QUANTITY A: -|x² + 1|
QUANTITY B: |x| + 1

In this case, quantity A will always be negative, and quantity B will always be positive, which means the correct answer is B.

Cheers,
Brent

### hi Brent! Could you please

hi Brent! Could you please explain the answer to this? I dont understand how you got the product of xy in your answer.

### Hi niveda94,

Hi niveda94,

I'm not sure what you're referring to. Did you mean to include a link with your question?

### Yes I did :) https:/

Yes I did :) https://gre.myprepclub.com/forum/root-9-root-80-root-9-root-18466.html

Q: How did you get the product of xy in your answer.

A: First I noticed that, in the original expression, we can:
Let x = √(9 + √80) and let y = √(9 - √80)

So, xy = √(9 + √80)√(9 - √80)

There's a square root property that says: (√j)(√k) = √(jk)
For example, (√4)(√9) = √36
Likewise, (√25)(√4) = √100

So, xy will equal the square root of (9 + √80)(9 - √80)
When we apply the FOIL method, (9 + √80)(9 - √80) = (9)(9) - 9√80 + 9√80 - √6400
= (9)(9) - √6400
= 81 - 80
= 1

Does that help?

### Hi Brent. What are we trying

Hi Brent. What are we trying to achieve when we do the same operations to both sides of a quantitative comparison question? Make one side 0? I am having trouble understanding the explanation concerning the following problem: https://gre.myprepclub.com/forum/0-x-7504.html where instructor adds 3x to both sides instead of subtracting (which is what i did). What was his thinking when doing this? I got the question correct but please help me understand this. Thanks

The great thing about the strategy is that there are many different ways to reach the same correct answer.

In my solution, I was applying two general strategies that often come in handy:
1) Move all the variables to one quantity
2) Set one of the quantities equal to zero

By applying those strategies I got to this point:
Quantity A: 0
Quantity B: x(4x + 3)
Since we're told x is positive, it's clear that quantity B is greater.

However, your strategy works as well. Let's start here:
Quantity A: -3x
Quantity B: 8x² + 3x

If we subtract 3x from both sides (as you did), we get:
Quantity A: -6x
Quantity B: 8x²

From here, since x is positive, it must be the case that Quantity A is negative and Quantity B is positive, in which case Quantity B is clearly greater.

### Hey Brent i have a question

Hey Brent i have a question how do i identify when to do foil here like (2+3)^2 we do normal add and sqaure but if (2x+2y)^2 due to varibles do we expand like quadratic?

### If the part in parentheses

If the part in parentheses can be simplified, then it's best to simplify before squaring.

For example, 2 + 3 can be simplified to equal 5, so it's better to write (2 + 3)² = (5)² = 25
Similarly, since 2k + 5k can be simplified to equal 7k, it's better to write (2k + 5k)² = (7k)² = 49k²

On the other hand, an expression like 2x + y can't be simplified.
So, we are forced to write (2x + y)² = (2x + y)(2x + y) = 4x² + 2xy + 2xy + y² = 4x² + 4xy + y²