How to use FOIL - PSAT Math
Card 0 of 42
Factor 2x2 - 5x – 12
Factor 2x2 - 5x – 12
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Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.
Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.
x > 0.
Quantity A: (x+3)(x-5)(x)
Quantity B: (x-3)(x-1)(x+3)
x > 0.
Quantity A: (x+3)(x-5)(x)
Quantity B: (x-3)(x-1)(x+3)
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Use FOIL:
(x+3)(x-5)(x) = (x2 - 5x + 3x - 15)(x) = x3 - 5x2 + 3x2 - 15x = x3 - 2x2 - 15x for A.
(x-3)(x-1)(x+3) = (x-3)(x+3)(x-1) = (x2 + 3x - 3x - 9)(x-1) = (x2 - 9)(x-1)
(x2 - 9)(x-1) = x3 - x2 - 9x + 9 for B.
The difference between A and B:
(x3 - 2x2 - 15x) - (x3 - x2 - 9x + 9) = x3 - 2x2 - 15x - x3 + x2 + 9x - 9
= - x2 - 4x - 9. Since all of the terms are negative and x > 0:
A - B < 0.
Rearrange A - B < 0:
A < B
Use FOIL:
(x+3)(x-5)(x) = (x2 - 5x + 3x - 15)(x) = x3 - 5x2 + 3x2 - 15x = x3 - 2x2 - 15x for A.
(x-3)(x-1)(x+3) = (x-3)(x+3)(x-1) = (x2 + 3x - 3x - 9)(x-1) = (x2 - 9)(x-1)
(x2 - 9)(x-1) = x3 - x2 - 9x + 9 for B.
The difference between A and B:
(x3 - 2x2 - 15x) - (x3 - x2 - 9x + 9) = x3 - 2x2 - 15x - x3 + x2 + 9x - 9
= - x2 - 4x - 9. Since all of the terms are negative and x > 0:
A - B < 0.
Rearrange A - B < 0:
A < B
Solve for all real values of 
.
Solve for all real values of
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First, move all terms to one side of the equation to set them equal to zero.
All terms contain an 
, so we can factor it out of the equation.
Now, we can factor the quadratic in parenthesis. We need two numbers that add to 
and multiply to 
.
We now have three terms that multiply to equal zero. One of these terms must equal zero in order for the product to be zero.
Our answer will be 
.
First, move all terms to one side of the equation to set them equal to zero.
All terms contain an
Now, we can factor the quadratic in parenthesis. We need two numbers that add to
We now have three terms that multiply to equal zero. One of these terms must equal zero in order for the product to be zero.
Our answer will be
Simplify: 
Simplify:
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In order to simplify this expression, you need to use the FOIL method. First rewrite the expression to look like this: 
Next, multiply your first terms together: 
Then, multiply your outside terms together: 
Then, multiply your inside terms together: 
Lastly, multiply your last terms together: 
Together, you have 
You can combine your like terms, 
, to give you the final answer: 
In order to simplify this expression, you need to use the FOIL method. First rewrite the expression to look like this:
Next, multiply your first terms together:
Then, multiply your outside terms together:
Then, multiply your inside terms together:
Lastly, multiply your last terms together:
Together, you have
You can combine your like terms,
Use FOIL to simplify the following product:
Use FOIL to simplify the following product:
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Use the FOIL method (first, outside, inside, last) to find the product of:
First: 
Outside: 
Inside: 
Last: 
Sum the products to find the polynomial:
Use the FOIL method (first, outside, inside, last) to find the product of:
First:
Outside:
Inside:
Last:
Sum the products to find the polynomial:
Simplify:
Simplify:
Tap to see back →
To solve this problem, use the FOIL method. Start by multiplying the First term in each set of parentheses: 
Then multiply the outside terms: 
Next, multiply the inside terms: 
Finally, multiply the last terms: 
When you put the pieces together, you have 
. Notice that the middle terms cancel each other out, and you are left with 
. When you distribute the two, you reach the answer: 
To solve this problem, use the FOIL method. Start by multiplying the First term in each set of parentheses:
Then multiply the outside terms:
Next, multiply the inside terms:
Finally, multiply the last terms:
When you put the pieces together, you have
Factor 2x2 - 5x – 12
Factor 2x2 - 5x – 12
Tap to see back →
Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.
Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.
x > 0.
Quantity A: (x+3)(x-5)(x)
Quantity B: (x-3)(x-1)(x+3)
x > 0.
Quantity A: (x+3)(x-5)(x)
Quantity B: (x-3)(x-1)(x+3)
Tap to see back →
Use FOIL:
(x+3)(x-5)(x) = (x2 - 5x + 3x - 15)(x) = x3 - 5x2 + 3x2 - 15x = x3 - 2x2 - 15x for A.
(x-3)(x-1)(x+3) = (x-3)(x+3)(x-1) = (x2 + 3x - 3x - 9)(x-1) = (x2 - 9)(x-1)
(x2 - 9)(x-1) = x3 - x2 - 9x + 9 for B.
The difference between A and B:
(x3 - 2x2 - 15x) - (x3 - x2 - 9x + 9) = x3 - 2x2 - 15x - x3 + x2 + 9x - 9
= - x2 - 4x - 9. Since all of the terms are negative and x > 0:
A - B < 0.
Rearrange A - B < 0:
A < B
Use FOIL:
(x+3)(x-5)(x) = (x2 - 5x + 3x - 15)(x) = x3 - 5x2 + 3x2 - 15x = x3 - 2x2 - 15x for A.
(x-3)(x-1)(x+3) = (x-3)(x+3)(x-1) = (x2 + 3x - 3x - 9)(x-1) = (x2 - 9)(x-1)
(x2 - 9)(x-1) = x3 - x2 - 9x + 9 for B.
The difference between A and B:
(x3 - 2x2 - 15x) - (x3 - x2 - 9x + 9) = x3 - 2x2 - 15x - x3 + x2 + 9x - 9
= - x2 - 4x - 9. Since all of the terms are negative and x > 0:
A - B < 0.
Rearrange A - B < 0:
A < B
Solve for all real values of .
Solve for all real values of
Tap to see back →
First, move all terms to one side of the equation to set them equal to zero.
All terms contain an , so we can factor it out of the equation.
Now, we can factor the quadratic in parenthesis. We need two numbers that add to and multiply to .
We now have three terms that multiply to equal zero. One of these terms must equal zero in order for the product to be zero.
Our answer will be .
First, move all terms to one side of the equation to set them equal to zero.
All terms contain an
Now, we can factor the quadratic in parenthesis. We need two numbers that add to
We now have three terms that multiply to equal zero. One of these terms must equal zero in order for the product to be zero.
Our answer will be
Simplify:
Simplify:
Tap to see back →
In order to simplify this expression, you need to use the FOIL method. First rewrite the expression to look like this:
Next, multiply your first terms together:
Then, multiply your outside terms together:
Then, multiply your inside terms together:
Lastly, multiply your last terms together:
Together, you have
You can combine your like terms, , to give you the final answer:
In order to simplify this expression, you need to use the FOIL method. First rewrite the expression to look like this:
Next, multiply your first terms together:
Then, multiply your outside terms together:
Then, multiply your inside terms together:
Lastly, multiply your last terms together:
Together, you have
You can combine your like terms,
Use FOIL to simplify the following product:
Use FOIL to simplify the following product:
Tap to see back →
Use the FOIL method (first, outside, inside, last) to find the product of:
First:
Outside:
Inside:
Last:
Sum the products to find the polynomial:
Use the FOIL method (first, outside, inside, last) to find the product of:
First:
Outside:
Inside:
Last:
Sum the products to find the polynomial:
Simplify:
Simplify:
Tap to see back →
To solve this problem, use the FOIL method. Start by multiplying the First term in each set of parentheses:
Then multiply the outside terms:
Next, multiply the inside terms:
Finally, multiply the last terms:
When you put the pieces together, you have . Notice that the middle terms cancel each other out, and you are left with . When you distribute the two, you reach the answer:
To solve this problem, use the FOIL method. Start by multiplying the First term in each set of parentheses:
Then multiply the outside terms:
Next, multiply the inside terms:
Finally, multiply the last terms:
When you put the pieces together, you have
Factor 2x2 - 5x – 12
Factor 2x2 - 5x – 12
Tap to see back →
Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.
Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.
x > 0.
Quantity A: (x+3)(x-5)(x)
Quantity B: (x-3)(x-1)(x+3)
x > 0.
Quantity A: (x+3)(x-5)(x)
Quantity B: (x-3)(x-1)(x+3)
Tap to see back →
Use FOIL:
(x+3)(x-5)(x) = (x2 - 5x + 3x - 15)(x) = x3 - 5x2 + 3x2 - 15x = x3 - 2x2 - 15x for A.
(x-3)(x-1)(x+3) = (x-3)(x+3)(x-1) = (x2 + 3x - 3x - 9)(x-1) = (x2 - 9)(x-1)
(x2 - 9)(x-1) = x3 - x2 - 9x + 9 for B.
The difference between A and B:
(x3 - 2x2 - 15x) - (x3 - x2 - 9x + 9) = x3 - 2x2 - 15x - x3 + x2 + 9x - 9
= - x2 - 4x - 9. Since all of the terms are negative and x > 0:
A - B < 0.
Rearrange A - B < 0:
A < B
Use FOIL:
(x+3)(x-5)(x) = (x2 - 5x + 3x - 15)(x) = x3 - 5x2 + 3x2 - 15x = x3 - 2x2 - 15x for A.
(x-3)(x-1)(x+3) = (x-3)(x+3)(x-1) = (x2 + 3x - 3x - 9)(x-1) = (x2 - 9)(x-1)
(x2 - 9)(x-1) = x3 - x2 - 9x + 9 for B.
The difference between A and B:
(x3 - 2x2 - 15x) - (x3 - x2 - 9x + 9) = x3 - 2x2 - 15x - x3 + x2 + 9x - 9
= - x2 - 4x - 9. Since all of the terms are negative and x > 0:
A - B < 0.
Rearrange A - B < 0:
A < B
Solve for all real values of .
Solve for all real values of
Tap to see back →
First, move all terms to one side of the equation to set them equal to zero.
All terms contain an , so we can factor it out of the equation.
Now, we can factor the quadratic in parenthesis. We need two numbers that add to and multiply to .
We now have three terms that multiply to equal zero. One of these terms must equal zero in order for the product to be zero.
Our answer will be .
First, move all terms to one side of the equation to set them equal to zero.
All terms contain an
Now, we can factor the quadratic in parenthesis. We need two numbers that add to
We now have three terms that multiply to equal zero. One of these terms must equal zero in order for the product to be zero.
Our answer will be
Simplify:
Simplify:
Tap to see back →
In order to simplify this expression, you need to use the FOIL method. First rewrite the expression to look like this:
Next, multiply your first terms together:
Then, multiply your outside terms together:
Then, multiply your inside terms together:
Lastly, multiply your last terms together:
Together, you have
You can combine your like terms, , to give you the final answer:
In order to simplify this expression, you need to use the FOIL method. First rewrite the expression to look like this:
Next, multiply your first terms together:
Then, multiply your outside terms together:
Then, multiply your inside terms together:
Lastly, multiply your last terms together:
Together, you have
You can combine your like terms,
Use FOIL to simplify the following product:
Use FOIL to simplify the following product:
Tap to see back →
Use the FOIL method (first, outside, inside, last) to find the product of:
First:
Outside:
Inside:
Last:
Sum the products to find the polynomial:
Use the FOIL method (first, outside, inside, last) to find the product of:
First:
Outside:
Inside:
Last:
Sum the products to find the polynomial:
Simplify:
Simplify:
Tap to see back →
To solve this problem, use the FOIL method. Start by multiplying the First term in each set of parentheses:
Then multiply the outside terms:
Next, multiply the inside terms:
Finally, multiply the last terms:
When you put the pieces together, you have . Notice that the middle terms cancel each other out, and you are left with . When you distribute the two, you reach the answer:
To solve this problem, use the FOIL method. Start by multiplying the First term in each set of parentheses:
Then multiply the outside terms:
Next, multiply the inside terms:
Finally, multiply the last terms:
When you put the pieces together, you have
Factor 2x2 - 5x – 12
Factor 2x2 - 5x – 12
Tap to see back →
Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.
Via the FOIL method, we can attest that x(2x) + x(3) + –4(2x) + –4(3) = 2x2 – 5x – 12.
x > 0.
Quantity A: (x+3)(x-5)(x)
Quantity B: (x-3)(x-1)(x+3)
x > 0.
Quantity A: (x+3)(x-5)(x)
Quantity B: (x-3)(x-1)(x+3)
Tap to see back →
Use FOIL:
(x+3)(x-5)(x) = (x2 - 5x + 3x - 15)(x) = x3 - 5x2 + 3x2 - 15x = x3 - 2x2 - 15x for A.
(x-3)(x-1)(x+3) = (x-3)(x+3)(x-1) = (x2 + 3x - 3x - 9)(x-1) = (x2 - 9)(x-1)
(x2 - 9)(x-1) = x3 - x2 - 9x + 9 for B.
The difference between A and B:
(x3 - 2x2 - 15x) - (x3 - x2 - 9x + 9) = x3 - 2x2 - 15x - x3 + x2 + 9x - 9
= - x2 - 4x - 9. Since all of the terms are negative and x > 0:
A - B < 0.
Rearrange A - B < 0:
A < B
Use FOIL:
(x+3)(x-5)(x) = (x2 - 5x + 3x - 15)(x) = x3 - 5x2 + 3x2 - 15x = x3 - 2x2 - 15x for A.
(x-3)(x-1)(x+3) = (x-3)(x+3)(x-1) = (x2 + 3x - 3x - 9)(x-1) = (x2 - 9)(x-1)
(x2 - 9)(x-1) = x3 - x2 - 9x + 9 for B.
The difference between A and B:
(x3 - 2x2 - 15x) - (x3 - x2 - 9x + 9) = x3 - 2x2 - 15x - x3 + x2 + 9x - 9
= - x2 - 4x - 9. Since all of the terms are negative and x > 0:
A - B < 0.
Rearrange A - B < 0:
A < B