How to use FOIL with the distributive property - ACT Math

Card 0 of 20

Question

Use FOIL on the following expression:

x(x + 1)(x – 1)

Answer

FOIL (First, Outside, Inside, Last): (x + 1)(x – 1) which is (x2 – 1) then multiply it by x, which is (x3 – x)

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Question

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

Answer

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

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Question

Distribute:

Answer

To FOIL using the distributive property, multiply the first terms together, then the outer terms, then the inner terms, and finally, the last terms.

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Question

Distribute:

Answer

FOIL using the distributive property:

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Question

Distribute:

Answer

FOIL using the distributive property:

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Question

Distribute:

Answer

FOIL using the distributive property.

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Question

Distribute:

Answer

FOIL using the distributive property.

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Question

Distribute:

Answer

FOIL using the distributive property.

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Question

Distribute:

Answer

Use the distributive property to FOIL

Simplify.

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Question

Distribute:

Answer

FOIL using the distributive property.

Simplify.

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Question

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

Answer

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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Question

Expand the following expression:

(f + 4) (f – 4)

Answer

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

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Question

Given that i2 = –1, what is the value of (6 + 3i)(6 – 3i)?

Answer

We start by foiling out the original equation, giving us 36 – 9(i2). Next, substitute 36 – 9(–1). This equals 36 + 9 = 45.

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Question

For all x, (4_x –_ 3)2 =

Answer

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.

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Question

Solve for .

Answer

To solve this equation, first distribute on the right side of the equation.

Then, subtract from both sides.

Then divide both sides by .

Another method for solving this problem is to plug in the answer choices and solve.

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Question

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?

Answer

The length is equal to W – 3

The area of a rectangle is length x width.

So W * (W – 3) = W2 – 3W

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Question

Expand the following expression:

(B – 2) (B + 4)

Answer

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

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Question

What is the product of the two real solutions of x2 + 5x = 6?

Answer

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.

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Question

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

Answer

Use FOIL: (2g – 3h)(2g – 3h) = 4g2 – 6gh – 6gh + 9h2 = 4g2 – 12gh + 9h2

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Question

FOIL:

Answer

By FOIL (First Outer Inner Last), we obtain –8_x_2 – 8_x_ – 6_x_ – 6.

Simplify: –8_x_2 – 14_x_ – 6

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