一个CT Math : FOIL
Study concepts, example questions & explanations for ACT Math
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Example Questions
Example Question #1 :How To Use Foil With The Distributive Property
For allx, (4x –3)2=
16x2+ 24x+ 9
16x2– 24x+ 9
12x2+ 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 #2 :How To Use Foil With The Distributive Property
Which of the following is equivalent to (2g – 3h)2?
4g2– 6gh + 9h2
4g2+ 9h2
4g2– 12gh + 9h2
4g2– 12gh + 3h2
g2– 12gh + 9h2
4g2– 12gh + 9h2
Use FOIL: (2g – 3h)(2g – 3h) = 4g2– 6gh – 6gh + 9h2= 4g2– 12gh + 9h2
Example Question #3 :How To Use Foil With The Distributive Property
Use FOIL on the following expression:
x(x + 1)(x – 1)
x3– x
x2– x
x3– x2
x
x – 1
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 #4 :How To Use Foil With The Distributive Property
繁殖:(4x+ 3)(2x+ 4)
8x² + 34
30x+ 12
8x² + 22x+12
6x² + 16x+ 24
3x² + 12x– 12
8x² + 22x+12
To solve you must use FOIL (first outer inner last)
Multiply 4xand 2x8 x²
Multiply 4xand 4 to get 16x
Multiply 3 and 2xto get 6x
Multiply 3 and 4 to get 12
一个dd the common terms and the awnser is 8x² + 22x+ 12
Example Question #5 :How To Use Foil With The Distributive Property
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
的refore,
Example Question #6 :How To Use Foil With The Distributive Property
Given that i2= –1, what is the value of (6 + 3i)(6 – 3i)?
36 + 9(i2)
36 – 9i
45
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 #7 :How To Use Foil With The Distributive Property
Expand the following expression:
(B – 2) (B + 4)
B2+ 2B + 8
B2+ 4B – 8
B2– 2B – 8
B2– 4B – 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
一个ll together this yields
B2+ 2B–8
Example Question #8 :How To Use Foil With The Distributive Property
一个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– 3
W2– 3W
W2– 3
2W – 3
2W2– 3W
W2– 3W
的length is equal to W – 3
的area of a rectangle is length x width.
So W * (W – 3) = W2– 3W
Example Question #9 :How To Use Foil With The Distributive Property
Expand the following expression:
(f + 4) (f – 4)
f2– 4f – 16
f2+ 16
2f – 4f – 16
f2– 16
f2+ 4f – 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
一个dding it all up:
f2– 4f +4f – 16
Example Question #10 :How To Use Foil With The Distributive Property
Expand the following expression: (x+3) (x+2)
2x + 5x + 6
x2+ 4x + 6
x2+ 5x + 3
x2+ 5x + 6
x2+ 3x + 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
一个dd it all together and we have x2+ 2x + 3x + 6
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