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Comment on FOIL Method for Expanding
12-2sqrt35 isn't 10sqrt35
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,
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?
Question link: https:/
Question link: https://gre.myprepclub.com/forum/which-is-greater-x-2-2-or-x-12433.html
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,
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?
Question link: https:/
Question link: https://gre.myprepclub.com/forum/which-is-greater-x-2-2-or-x-12433.html
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 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:/
Solution link: https:/
Solution link: https://gre.myprepclub.com/forum/root-9-root-80-root-9-root-18466.html#p...
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
Question link: https:/
Question link: https://gre.myprepclub.com/forum/0-x-7504.html
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
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
Hi Brent, could you help with
https://gre.myprepclub.com/forum/one-of-the-roots-of-the-equation-x-2-kx-3169.html#p105976
x^2+kx-6=0 is 3
If I had use FOIL, I got (x+3)(x-2) due to k is positive here therefore I make 3 as positive
but then I will get x=-3 or x=2, which doesn't match with the given condition of one the root is 3.
Where has the reasoning gone wrong here or we should ignore +/- sign in the given x^2+kx-6=0 here ?
Could you help clarify? Thanks Brent
Hi Kim.
Hi Kim.
I responded to your question here: https://gre.myprepclub.com/forum/one-of-the-roots-of-the-equation-x-2-kx...