Exponents and the Distributive Property - GRE Quantitative Reasoning
Card 0 of 80
Expand the following equation:
Expand the following equation:
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use FOIL to factor the expression.
First: (x3)(x) = x4
Outside (x3)(7) = 7x3
Inside (–3)(x) = –3x (Don't forget the negatives!)
Last (3)(7) = –21
use FOIL to factor the expression.
First: (x3)(x) = x4
Outside (x3)(7) = 7x3
Inside (–3)(x) = –3x (Don't forget the negatives!)
Last (3)(7) = –21
Quantity A: 
Quantity B: 
Quantity A:
Quantity B:
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The difference of squares formula says (x + a)(x - a) = x2 - a2.
Thus, Quantity A equals 8.
Therefore, Quantity B is greater.
The difference of squares formula says (x + a)(x - a) = x2 - a2.
Thus, Quantity A equals 8.
Therefore, Quantity B is greater.
What is the value of t if: 3x2 + tx - 21 = (3x - 3)(x + 7)?
What is the value of t if: 3x2 + tx - 21 = (3x - 3)(x + 7)?
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Use the foil method: (3x - 3) (x + 7) = 3x2 +21x - 3x - 21 = 3x2 +18x -21 so t = 18.
Use the foil method: (3x - 3) (x + 7) = 3x2 +21x - 3x - 21 = 3x2 +18x -21 so t = 18.
Quantitative Comparison
Quantity A: 
Quantity B: 
Quantitative Comparison
Quantity A:
Quantity B:
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Quantity A: 22 + 32 = 4 + 9 = 13
Quantity B: (2 + 3)2 = 52 = 25, so Quantity B is greater.
We can also think of this in more general terms. _x_2 + _y_2 does not generally equal (x + y)2.
Quantity A: 22 + 32 = 4 + 9 = 13
Quantity B: (2 + 3)2 = 52 = 25, so Quantity B is greater.
We can also think of this in more general terms. _x_2 + _y_2 does not generally equal (x + y)2.
Expand the function:
Expand the function:
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Use the method of FOIL (First, Outside, Inside, Last) and add exponents for like bases:
Use the method of FOIL (First, Outside, Inside, Last) and add exponents for like bases:
Quantity A: 
Quantity B: 
Quantity A:
Quantity B:
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To approach this problem, consider the two quantities
Quantity A: 
Quantity B: 
They are in different forms, so expand quantity A:
Quantity A: 
Quantity B: 
Now, for the purpose of comparison, subtract shared terms from each quantity:
Quantity A*: 
Quantity B*: 
Both 
and 
are negative, non-zero values. Since 
is a product of two negative values, it must be positive. Quantity B must be greater than Quantity A.
To approach this problem, consider the two quantities
Quantity A:
Quantity B:
They are in different forms, so expand quantity A:
Quantity A:
Quantity B:
Now, for the purpose of comparison, subtract shared terms from each quantity:
Quantity A*:
Quantity B*:
Both
Quantity A: 
Quantity B: 
Quantity A:
Quantity B:
Tap to see back →
Begin by expanding Quantity A:
Now in order to compare this to Quantity B:
A good method would be to subtract shared terms from each Quantity; in this case, both quantities have an 
and 
term. Removing them gives:
Quantity A' : 
Quantity B' : 
The question now is the sign of Quantity A'; if it's always positive, Quantity A is greater. If it's always negative, Quantity B is greater. If it is zero, the two are the same.
We only know that
If 
, then Quantity A' would be zero.
If 
, then Quantity A' would be positive.
Since values of x and y can be chosen to vary the relationship, th relationship cannot be determined.
Begin by expanding Quantity A:
Now in order to compare this to Quantity B:
A good method would be to subtract shared terms from each Quantity; in this case, both quantities have an
Quantity A' :
Quantity B' :
The question now is the sign of Quantity A'; if it's always positive, Quantity A is greater. If it's always negative, Quantity B is greater. If it is zero, the two are the same.
We only know that
If
If
Since values of x and y can be chosen to vary the relationship, th relationship cannot be determined.
Quantity A: 
Quantity B: 
Quantity A:
Quantity B:
Tap to see back →
Begin by expanding Quantity A:
Now in order to compare this to Quantity B:
A good method would be to subtract shared terms from each Quantity; in this case, both quantities have an 
and 
term. Removing them gives:
Quantity A' : 
Quantity B' : 
The question now is the sign of Quantity A'; if it's always positive, Quantity A is greater. If it's always negative, Quantity B is greater. If it is zero, the two are the same.
We know that
Now compare 
and 
:
Looking at absolute values so that we're only considering positive terms:
From this it follows that by multiplying 
across the inequality :
From this we can determine that the magnitude of 
is greater. However, since this is the product of one negative number and two positive numbers, 
is negative, and the sum of 
and 
must in turn be negative, and so Quantity A' must be negative!
From this we can say that Quantity B is greater.
Begin by expanding Quantity A:
Now in order to compare this to Quantity B:
A good method would be to subtract shared terms from each Quantity; in this case, both quantities have an
Quantity A' :
Quantity B' :
The question now is the sign of Quantity A'; if it's always positive, Quantity A is greater. If it's always negative, Quantity B is greater. If it is zero, the two are the same.
We know that
Now compare
Looking at absolute values so that we're only considering positive terms:
From this it follows that by multiplying
From this we can determine that the magnitude of
From this we can say that Quantity B is greater.
Quantity A: 
Quantity B: 
Quantity A:
Quantity B:
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This problem is deceptive. Looking at Quantity A, one may think to factor and reduce it as follows:
Which is identical to Quantity B.
However, we cannot ignore that 
in the original fraction! We are given no conditions as to the value of 
. If 
, then Quantity A would be undefined. Since we're not given the condition 
, we cannot ignore this possibility.
The relationship cannot be established.
This problem is deceptive. Looking at Quantity A, one may think to factor and reduce it as follows:
Which is identical to Quantity B.
However, we cannot ignore that
The relationship cannot be established.
Solve the following expression, 
.
Solve the following expression,
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You must FOIL the expression which means to multiply the first terms together followed by the outer terms, then the inner terms and lastly, the last terms.
The expression written out looks like
.
You multiple both First terms to get 
.
Then the outer terms are multiplied 
.
Then you multiple the inner terms together 
.
Finally you multiply the last terms of each 
.
This gives you 
or 
.
You must FOIL the expression which means to multiply the first terms together followed by the outer terms, then the inner terms and lastly, the last terms.
The expression written out looks like
You multiple both First terms to get
Then the outer terms are multiplied
Then you multiple the inner terms together
Finally you multiply the last terms of each
This gives you
Expand the following equation:
Expand the following equation:
Tap to see back →
use FOIL to factor the expression.
First: (x3)(x) = x4
Outside (x3)(7) = 7x3
Inside (–3)(x) = –3x (Don't forget the negatives!)
Last (3)(7) = –21
use FOIL to factor the expression.
First: (x3)(x) = x4
Outside (x3)(7) = 7x3
Inside (–3)(x) = –3x (Don't forget the negatives!)
Last (3)(7) = –21
Quantity A:
Quantity B:
Quantity A:
Quantity B:
Tap to see back →
The difference of squares formula says (x + a)(x - a) = x2 - a2.
Thus, Quantity A equals 8.
Therefore, Quantity B is greater.
The difference of squares formula says (x + a)(x - a) = x2 - a2.
Thus, Quantity A equals 8.
Therefore, Quantity B is greater.
What is the value of t if: 3x2 + tx - 21 = (3x - 3)(x + 7)?
What is the value of t if: 3x2 + tx - 21 = (3x - 3)(x + 7)?
Tap to see back →
Use the foil method: (3x - 3) (x + 7) = 3x2 +21x - 3x - 21 = 3x2 +18x -21 so t = 18.
Use the foil method: (3x - 3) (x + 7) = 3x2 +21x - 3x - 21 = 3x2 +18x -21 so t = 18.
Quantitative Comparison
Quantity A:
Quantity B:
Quantitative Comparison
Quantity A:
Quantity B:
Tap to see back →
Quantity A: 22 + 32 = 4 + 9 = 13
Quantity B: (2 + 3)2 = 52 = 25, so Quantity B is greater.
We can also think of this in more general terms. _x_2 + _y_2 does not generally equal (x + y)2.
Quantity A: 22 + 32 = 4 + 9 = 13
Quantity B: (2 + 3)2 = 52 = 25, so Quantity B is greater.
We can also think of this in more general terms. _x_2 + _y_2 does not generally equal (x + y)2.
Expand the function:
Expand the function:
Tap to see back →
Use the method of FOIL (First, Outside, Inside, Last) and add exponents for like bases:
Use the method of FOIL (First, Outside, Inside, Last) and add exponents for like bases:
Quantity A:
Quantity B:
Quantity A:
Quantity B:
Tap to see back →
To approach this problem, consider the two quantities
Quantity A:
Quantity B:
They are in different forms, so expand quantity A:
Quantity A:
Quantity B:
Now, for the purpose of comparison, subtract shared terms from each quantity:
Quantity A*:
Quantity B*:
Both and are negative, non-zero values. Since is a product of two negative values, it must be positive. Quantity B must be greater than Quantity A.
To approach this problem, consider the two quantities
Quantity A:
Quantity B:
They are in different forms, so expand quantity A:
Quantity A:
Quantity B:
Now, for the purpose of comparison, subtract shared terms from each quantity:
Quantity A*:
Quantity B*:
Both
Quantity A:
Quantity B:
Quantity A:
Quantity B:
Tap to see back →
Begin by expanding Quantity A:
Now in order to compare this to Quantity B:
A good method would be to subtract shared terms from each Quantity; in this case, both quantities have an and term. Removing them gives:
Quantity A' :
Quantity B' :
The question now is the sign of Quantity A'; if it's always positive, Quantity A is greater. If it's always negative, Quantity B is greater. If it is zero, the two are the same.
We only know that
If , then Quantity A' would be zero.
If , then Quantity A' would be positive.
Since values of x and y can be chosen to vary the relationship, th relationship cannot be determined.
Begin by expanding Quantity A:
Now in order to compare this to Quantity B:
A good method would be to subtract shared terms from each Quantity; in this case, both quantities have an
Quantity A' :
Quantity B' :
The question now is the sign of Quantity A'; if it's always positive, Quantity A is greater. If it's always negative, Quantity B is greater. If it is zero, the two are the same.
We only know that
If
If
Since values of x and y can be chosen to vary the relationship, th relationship cannot be determined.
Quantity A:
Quantity B:
Quantity A:
Quantity B:
Tap to see back →
Begin by expanding Quantity A:
Now in order to compare this to Quantity B:
A good method would be to subtract shared terms from each Quantity; in this case, both quantities have an and term. Removing them gives:
Quantity A' :
Quantity B' :
The question now is the sign of Quantity A'; if it's always positive, Quantity A is greater. If it's always negative, Quantity B is greater. If it is zero, the two are the same.
We know that
Now compare and :
Looking at absolute values so that we're only considering positive terms:
From this it follows that by multiplying across the inequality :
From this we can determine that the magnitude of is greater. However, since this is the product of one negative number and two positive numbers, is negative, and the sum of and must in turn be negative, and so Quantity A' must be negative!
From this we can say that Quantity B is greater.
Begin by expanding Quantity A:
Now in order to compare this to Quantity B:
A good method would be to subtract shared terms from each Quantity; in this case, both quantities have an
Quantity A' :
Quantity B' :
The question now is the sign of Quantity A'; if it's always positive, Quantity A is greater. If it's always negative, Quantity B is greater. If it is zero, the two are the same.
We know that
Now compare
Looking at absolute values so that we're only considering positive terms:
From this it follows that by multiplying
From this we can determine that the magnitude of
From this we can say that Quantity B is greater.
Quantity A:
Quantity B:
Quantity A:
Quantity B:
Tap to see back →
This problem is deceptive. Looking at Quantity A, one may think to factor and reduce it as follows:
Which is identical to Quantity B.
However, we cannot ignore that in the original fraction! We are given no conditions as to the value of . If , then Quantity A would be undefined. Since we're not given the condition , we cannot ignore this possibility.
The relationship cannot be established.
This problem is deceptive. Looking at Quantity A, one may think to factor and reduce it as follows:
Which is identical to Quantity B.
However, we cannot ignore that
The relationship cannot be established.
Solve the following expression, .
Solve the following expression,
Tap to see back →
You must FOIL the expression which means to multiply the first terms together followed by the outer terms, then the inner terms and lastly, the last terms.
The expression written out looks like
.
You multiple both First terms to get .
Then the outer terms are multiplied .
Then you multiple the inner terms together .
Finally you multiply the last terms of each .
This gives you or .
You must FOIL the expression which means to multiply the first terms together followed by the outer terms, then the inner terms and lastly, the last terms.
The expression written out looks like
You multiple both First terms to get
Then the outer terms are multiplied
Then you multiple the inner terms together
Finally you multiply the last terms of each
This gives you