ACT Math : Algebra
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Example Questions
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 #3 : Distributive Property
Expand the following expression:
(B – 2) (B + 4)
B2 + 4B – 8
B2 + 2B + 8
B2 – 2B – 8
B2 + 2B – 8
B2 – 4B – 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 #4 : Distributive Property
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?
2W2 – 3W
2W2 – 3
W2 – 3
W2 – 3W
2W – 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
Example Question #11 : How To Use Foil With The Distributive Property
FOIL:
By FOIL (First Outer Inner Last), we obtain –8x2 – 8x – 6x – 6.
Simplify: –8x2 – 14x – 6
Example Question #11 : Distributive Property
What is the product of the two real solutions of x2 + 5x = 6?
6
–1
1
–6
–6
x2 + 5x – 6 = 0 factors to (x+6)(x–1) = 0.
Therefore, the two real solutions are x = –6 and x = 1. Their product is simply –6.
Example Question #13 : How To Use Foil With The Distributive Property
What is the value of (5 + 3i)(6 – 2i)?
12 + 8i
24 + 8i
20 – 8i
16 – 2i
36 + 8i
36 + 8i
We FOIL the equation to obtain 30 – 10i + 18i – 6i2, combining like terms and substituting i2 = –1, we obtain 36 + 8i.
Example Question #12 : Foil
Expand the following expression:
FOIL 
Then multiply it by 
Example Question #12 : Distributive Property
Expand using FOIL:
Step One: Expand
Step 2: Use the FOIL method
First:
Outside:
Inside:
Last:
Sum the products:
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