### All ACT Math Resources

## Example Questions

### Example Question #1 : Foil

For all *x*, (4*x –* 3)^{2} =

**Possible Answers:**

12*x*^{2 }+ 24*x –* 9

16*x*^{2 }+ 9

16*x*^{2 }– 24*x *+ 9

16*x*^{2 }– 9

16*x*^{2 }+ 24*x *+ 9

**Correct answer:**

16*x*^{2 }– 24*x *+ 9

To solve this problem, you should FOIL: (4*x* – 3)(4*x* – 3) = 16*x*^{2 }– 12*x –* 12*x *+ 9 = 16*x*^{2 }– 24*x *+ 9.

### Example Question #1 : Distributive Property

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

**Possible Answers:**

4g^{2 }+ 9h^{2}

4g^{2 }– 6gh + 9h^{2}

4g^{2 }– 12gh + 3h^{2}

4g^{2 }– 12gh + 9h^{2}

g^{2 }– 12gh + 9h^{2}

**Correct answer:**

4g^{2 }– 12gh + 9h^{2}

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

### Example Question #2 : Distributive Property

Use FOIL on the following expression:

x(x + 1)(x – 1)

**Possible Answers:**

x^{2 }– x

x – 1

x

x^{3 }– x

x^{3 }– x^{2}

**Correct answer:**

x^{3 }– x

FOIL (First, Outside, Inside, Last): (x + 1)(x – 1) which is (x^{2 }– 1) then multiply it by x, which is (x^{3 }– x)

### Example Question #1 : Foil

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

**Possible Answers:**

3*x*² + 12*x* – 12

8*x*² + 34

6*x*² + 16*x* + 24

8*x*² + 22*x* +12

30*x* + 12

**Correct answer:**

8*x*² + 22*x* +12

To solve you must use FOIL (first outer inner last)

Multiply 4*x* and 2*x* to get 8x²

Multiply 4*x* and 4 to get 16*x*

Multiply 3 and 2*x* to get 6*x*

Multiply 3 and 4 to get 12

Add the common terms and the awnser is 8*x*² + 22*x* + 12

### Example Question #1 : Foil

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

**Possible Answers:**

**Correct answer:**

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 #1 : Foil

Given that i^{2 }= –1, what is the value of (6 + 3i)(6 – 3i)?

**Possible Answers:**

25

45

36 + 9i

36 + 9(i^{2})

36 – 9i

**Correct answer:**

45

We start by foiling out the original equation, giving us 36 – 9(i^{2}). Next, substitute 36 – 9(–1). This equals 36 + 9 = 45.

### Example Question #3 : Distributive Property

Expand the following expression:

(B – 2) (B + 4)

**Possible Answers:**

B^{2} + 2B – 8

B^{2} – 4B – 8

B^{2} + 2B + 8

B^{2} + 4B – 8

B^{2} – 2B – 8

**Correct answer:**

B^{2} + 2B – 8

Here we use FOIL:

Firsts: B * B = B^{2}

Outer: B * 4 = 4B

Inner: –2 * B = –2B

Lasts: –2 * 4 = –8

All together this yields

B^{2} + 2B *–* 8

### Example Question #2 : 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?

**Possible Answers:**

2W^{2} – 3W

2W^{2} – 3

W^{2} – 3W

W^{2} – 3

2W – 3

**Correct answer:**

W^{2} – 3W

The length is equal to W – 3

The area of a rectangle is length x width.

So W * (W – 3) = W^{2} – 3W

### Example Question #2 : Foil

Expand the following expression:

(f + 4) (f – 4)

**Possible Answers:**

f^{2} – 4f – 16

f^{2} + 16

f^{2} + 4f – 16

f^{2} – 16

2f – 4f – 16

**Correct answer:**

f^{2} – 16

using FOIL:

First: f x f = f^{2}

Outer: f x – 4 = –4f

Intter: 4 x f = 4f

Lasts: 4 x – 4 = –16

Adding it all up:

f^{2} – 4f +4f – 16

### Example Question #1 : Foil

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

**Possible Answers:**

x^{2} + 5x + 3

x^{2} + 5x + 6

x^{2} + 3x + 6

x^{2} + 4x + 6

2x + 5x + 6

**Correct answer:**

x^{2} + 5x + 6

This simply requires us to recall our rules from FOIL

First: X multiplied by X yields x^{2}

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 x^{2 }+ 2x + 3x + 6

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