How to use FOIL with the distributive property - ACT Math

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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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Question

What is the value of (5 + 3_i_)(6 – 2_i_)?

Answer

We FOIL the equation to obtain 30 – 10_i_ + 18_i_ – 6_i_2, combining like terms and substituting i_2 = –1, we obtain 36 + 8_i.

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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

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

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 .

$\frac{4x}{4}=\frac{-12}{4}$

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: (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:

$(2x)(x+1)^{2}$

Answer

FOIL $(x+1)^{2}$ and we get:

$(x^{2}+2x+1)$

Then multiply it by and get:

$(2x^{3}+4x^{2}+2x)$

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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

Multiply the complex numbers:

$(3+4i)(2+8i)$ .

Answer

Expanding out gives $6+24i+8i+32i^{2}$ .

We know that $i=\sqrt{-1}$ so when we substitute that in we get $6+32i-32$ .

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Question

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

$(x^{2} + 4x)(5x - 2x)$

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: ⋅

$(x^{2} + 4x)(5x - 2x)$

First: $x^{2} \cdot 5x = 5x^{3}$

Outside: $x^{2} \cdot -2x = -2x^{3}$

Inside: $4x \cdot 5x = 20x^{2}$

Last: $4x \cdot -2x = -8x^{2}$

Now add all of the terms together:

$5x^{3} - 2x^{3} +20x^{2} -8x^{2}$

Which simplifies to:

$3x^{3} +12x^{2}$

Now, we must see what is greatest common factor shared between each of these two terms. They are both divisible by as well as $x^{2}$ .

Therefore, $3x^{2}$ is the greatest common factor.

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Question

Use the FOIL method to find the product. The answer must be in standard form.

Answer

Use the FOIL method to find the product. The answer must be in standard form.

Step 1: Use the FOIL method

First: $x^3\cdot x^6=x^9$

Outside: $x^3\cdot9x^2=9x^5$

Inside: $2x\cdot x^6=2x^7$

Last: $2x \cdot 9x^2=18x^3$

Add these to find the product:

Step 2: Write the product in standard form

Standard form means the terms are written from highest degree to lowest degree. You find the degree of a term by adding the exponents in the term.

Therefore:

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