ACT Math : How to use FOIL with the distributive property

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #1 : How To Use Foil With The Distributive Property

For all x, (4x – 3)2 =

Possible Answers:

12x+ 24x – 9

16x+ 9

16x+ 24+ 9

16x– 9

16x– 24+ 9

Correct answer:

16x– 24+ 9

Explanation:

To solve this problem, you should FOIL: (4x – 3)(4x – 3) = 16x– 12x – 12+ 9 = 16x– 24+ 9. 

Example Question #1094 : Algebra

Which of the following is equivalent to (2g – 3h)2?

Possible Answers:

4g– 6gh + 9h2

4g– 12gh + 3h2

g– 12gh + 9h2

4g– 12gh + 9h2

4g+ 9h2

Correct answer:

4g– 12gh + 9h2

Explanation:

Use FOIL: (2g – 3h)(2g – 3h) = 4g– 6gh – 6gh + 9h= 4g– 12gh + 9h2

Example Question #3 : Foil

Use FOIL on the following expression:

x(x + 1)(x – 1)

Possible Answers:

x – 1

x

x– x2

x– x

x– x

Correct answer:

x– x

Explanation:

FOIL (First, Outside, Inside, Last): (x + 1)(x – 1) which is (x– 1) then multiply it by x, which is (x– x)

Example Question #2 : Distributive Property

Multiply: (4x + 3)(2x + 4)

Possible Answers:

30x + 12

6x² + 16x + 24

8x² + 34

3x² + 12x – 12

8x² + 22x +12

Correct answer:

8x² + 22x +12

Explanation:

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 #3 : Foil

What is the greatest common factor in the evaluated expression below?

Possible Answers:

Correct answer:

Explanation:

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  as well as .

Therefore,  is the greatest common factor.

Example Question #2 : Distributive Property

Given that i= –1, what is the value of (6 + 3i)(6 – 3i)?

Possible Answers:

25

36 + 9(i2)

36 – 9i

45

36 + 9i

Correct answer:

45

Explanation:

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 : How To Use Foil With The Distributive Property

Expand the following expression:

(B – 2) (B + 4)

Possible Answers:

B2 – 4B – 8

B2 + 4B – 8

B2 + 2B + 8

B2 – 2B – 8

B2 + 2B – 8

Correct answer:

B2 + 2B – 8

Explanation:

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 : How To Use Foil With The 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?

Possible Answers:

W2 – 3W

2W – 3

2W2 – 3

2W2 – 3W

W2 – 3

Correct answer:

W2 – 3W

Explanation:

The length is equal to W – 3

 

The area of a rectangle is length x width.

 

So W * (W – 3) = W2 – 3W

Example Question #4 : How To Use Foil With The Distributive Property

Expand the following expression: 

(f + 4) (f – 4)

Possible Answers:

f2 + 16

f2 + 4f – 16

f2 – 16

2f – 4f – 16

f2 – 4f – 16

Correct answer:

f2 – 16

Explanation:

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 #3 : How To Use Foil With The Distributive Property

Expand the following expression: (x+3) (x+2)

 

Possible Answers:

x2 + 5x + 3

x2 + 3x + 6

x2 + 4x + 6

x2 + 5x + 6

2x + 5x + 6

Correct answer:

x2 + 5x + 6

Explanation:

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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