How to use FOIL - SAT Math
Card 0 of 5
Factor 2x2 - 5x – 12
Factor 2x2 - 5x – 12
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.
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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)
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
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Solve for all real values of 
.
Solve for all real values of
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
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Find the product in terms of 
:
Find the product in terms of
This question can be solved using the FOIL method. So the first terms are multiplied together:
This gives:
The x-squared is due to the x times x.
The outer terms are then multipled together and added to the value above.
The inner two terms are multipled together to give the next term of the expression.
Finally the last terms are multiplied together.
All of the above terms are added together to give:
Combining like terms gives
.
This question can be solved using the FOIL method. So the first terms are multiplied together:
This gives:
The x-squared is due to the x times x.
The outer terms are then multipled together and added to the value above.
The inner two terms are multipled together to give the next term of the expression.
Finally the last terms are multiplied together.
All of the above terms are added together to give:
Combining like terms gives
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Expand the following expression:
Expand the following expression:
Expand the following expression:
Let's begin by recalling the meaning of FOIL: First, Outer, Inner, Last.
This means that in a situation such as we are given here, we need to multiply all the terms in a particular way. FOIL makes it easy to remember to multiply each pair of terms.
Let's begin:
First:
Outer:
Inner:
Last:
Now, put it together in standard form to get:
Expand the following expression:
Let's begin by recalling the meaning of FOIL: First, Outer, Inner, Last.
This means that in a situation such as we are given here, we need to multiply all the terms in a particular way. FOIL makes it easy to remember to multiply each pair of terms.
Let's begin:
First:
Outer:
Inner:
Last:
Now, put it together in standard form to get:
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