ACT Math : How to use FOIL with the distributive property
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Example Questions
Example Question #1 : Foil
For all x, (4x – 3)2 =
12x2 + 24x – 9
16x2 – 24x + 9
16x2 + 24x + 9
16x2 + 9
16x2 – 9
16x2 – 24x + 9
To solve this problem, you should FOIL: (4x – 3)(4x – 3) = 16x2 – 12x – 12x + 9 = 16x2 – 24x + 9.
Example Question #1 : Foil
Which of the following is equivalent to (2g – 3h)2?
4g2 – 12gh + 3h2
4g2 + 9h2
4g2 – 12gh + 9h2
g2 – 12gh + 9h2
4g2 – 6gh + 9h2
4g2 – 12gh + 9h2
Use FOIL: (2g – 3h)(2g – 3h) = 4g2 – 6gh – 6gh + 9h2 = 4g2 – 12gh + 9h2
Example Question #2 : Distributive Property
Use FOIL on the following expression:
x(x + 1)(x – 1)
x3 – x2
x
x – 1
x3 – x
x2 – x
x3 – x
FOIL (First, Outside, Inside, Last): (x + 1)(x – 1) which is (x2 – 1) then multiply it by x, which is (x3 – x)
Example Question #2 : Distributive Property
Multiply: (4x + 3)(2x + 4)
8x² + 34
6x² + 16x + 24
8x² + 22x +12
3x² + 12x – 12
30x + 12
8x² + 22x +12
To solve you must use FOIL (first outer inner last)
Multiply 4x and 2x to get 8x²
Multiply 4x and 4 to get 16x
Multiply 3 and 2x to get 6x
Multiply 3 and 4 to get 12
Add the common terms and the awnser is 8x² + 22x + 12
Example Question #2 : Foil
What is the greatest common factor in the evaluated expression below?
This is essentially a multi-part question that at first may seem confusing, until it's realized that the question only involves basic algebra, or more specifically, using FOIL and greatest common factor concepts.
First, we must use FOIL (first, outside, inside, last), to evaluate the given expression: ⋅
First:
Outside:
Inside:
Last:
Now add all of the terms together:
Which simplifies to:
Now, we must see what is greatest common factor shared between each of these two terms. They are both divisible by 
Therefore, 
Example Question #5 : Foil
Given that i2 = –1, what is the value of (6 + 3i)(6 – 3i)?
45
36 – 9i
36 + 9(i2)
36 + 9i
25
45
We start by foiling out the original equation, giving us 36 – 9(i2). Next, substitute 36 – 9(–1). This equals 36 + 9 = 45.
Example Question #2 : Foil
Expand the following expression:
(B – 2) (B + 4)
B2 + 2B – 8
B2 + 4B – 8
B2 – 4B – 8
B2 + 2B + 8
B2 – 2B – 8
B2 + 2B – 8
Here we use FOIL:
Firsts: B * B = B2
Outer: B * 4 = 4B
Inner: –2 * B = –2B
Lasts: –2 * 4 = –8
All together this yields
B2 + 2B – 8
Example Question #3 : Foil
A rectangle's length L is 3 inches shorter than its width, W. What is an appropriate expression for the area of the rectangle in terms of W?
2W – 3
W2 – 3
2W2 – 3W
W2 – 3W
2W2 – 3
W2 – 3W
The length is equal to W – 3
The area of a rectangle is length x width.
So W * (W – 3) = W2 – 3W
Example Question #8 : Foil
Expand the following expression:
(f + 4) (f – 4)
f2 – 4f – 16
f2 – 16
2f – 4f – 16
f2 + 4f – 16
f2 + 16
f2 – 16
using FOIL:
First: f x f = f2
Outer: f x – 4 = –4f
Intter: 4 x f = 4f
Lasts: 4 x – 4 = –16
Adding it all up:
f2 – 4f +4f – 16
Example Question #9 : Foil
Expand the following expression: (x+3) (x+2)
x2 + 4x + 6
2x + 5x + 6
x2 + 3x + 6
x2 + 5x + 3
x2 + 5x + 6
x2 + 5x + 6
This simply requires us to recall our rules from FOIL
First: X multiplied by X yields x2
Outer: X multplied by 2 yields 2x
Inner: 3 multiplied by x yields 3x
Lasts: 2 multiplied by 3 yields 6
Add it all together and we have x2 + 2x + 3x + 6
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