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ACT Math : Distributive Property

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Example Questions

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Example Question #2632 : Act Math

Distribute:

(6x-2)(3x+3)

Possible Answers:

18x^2-12x-6

9x^2-12x-6

12x^2-9x-6

18x^2+12x-6

Correct answer:

18x^2+12x-6

Explanation:

FOIL using the distributive property.

18x^2+18x-6x-6

Simplify.

18x^2+12x-6

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Example Question #52 : How To Use Foil With The Distributive Property

Distribute and simplify: (3x-1)(x+2)

Possible Answers:

4x-2

3x^2 + 5x - 2

8x + 2

4x^2 - 2

3x^2 - 5x + 2

Correct answer:

3x^2 + 5x - 2

Explanation:

To FOIL this binomial distribution, we simply distribute the terms in a specific order:

Multiply the First terms:

$3x\cdot x = 3x^2$

Multiply the Outer terms:

$3x\cdot 2 = 6x$

Multiply the Inner terms:

$-1\cdot x = -x$

Multiply the Last terms:

$-1\cdot 2 = -2$

Lastly, combine any terms that allow this (usually, but not always, the two middle terms):

6x-x = 5x

Arrange your answer in descending exponential form, and you're done.

(3x-1)(x+2) = 3x^2 + 5x - 2

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Example Question #53 : How To Use Foil With The Distributive Property

What is the simplified form of (x+7)(x-7) ?

Possible Answers:

x^2 - 49

x^2 + 49

x^2 -14x - 49

14x - 7

Correct answer:

x^2 - 49

Explanation:

To FOIL this binomial distribution, we simply distribute the terms in a specific order:

(x+7)(x-7)

Multiply the First terms:

$x\cdot x = x^2$

Multiply the Outer terms:

$x \cdot -7 = -7x$

Multiply the Inner terms:

$7 \cdot x = 7x$

Multiply the Last terms:

$7 \cdot -7 = -49$

Lastly, combine any terms that allow this (usually, but not always, the two middle terms):

7x -7x = 0

Arrange your answer in descending exponential form, and you're done.

(x+7)(x-7) = x^2 - 49

Notice that this answer is also a difference of squares.

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Example Question #54 : How To Use Foil With The Distributive Property

Distribute and simplify: (x-7)(4x-2)

Possible Answers:

4x^2 -30x + 14

5x +30x - 14

4x^2 -26x + 14

5x -30x - 14

4x^2 -30x - 14

Correct answer:

4x^2 -30x + 14

Explanation:

To FOIL this binomial distribution, we simply distribute the terms in a specific order:

(x-7)(4x-2)

Multiply the First terms:

$x\cdot 4x = 4x^2$

Multiply the Outer terms:

$x\cdot -2 = -2x$

Multiply the Inner terms:

$-7\cdot 4x = -28x$

Multiply the Last terms:

$-7\cdot -2 = 14$

Lastly, combine any terms that allow this (usually, but not always, the two middle terms):

-2x-28x = -30x

Arrange your answer in descending exponential form, and you're done.

(x-7)(4x-2)= 4x^2 -30x + 14

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Example Question #55 : How To Use Foil With The Distributive Property

Distribute and simplify: (7x+5)(2x+5)

Possible Answers:

9x^2 + 45x +25

14x^2 + 25x +25

9x^2 + 25x +25

14x^2 + 45x +10

14x^2 + 45x +25

Correct answer:

14x^2 + 45x +25

Explanation:

To FOIL this binomial distribution, we simply distribute the terms in a specific order:

(7x+5)(2x+5)

Multiply the First terms:

$7x\cdot 2x = 14x^2$

Multiply the Outer terms:

$7x\cdot 5 = 35x$

Multiply the Inner terms:

$5\cdot 2x = 10x$

Multiply the Last terms:

$5\cdot 5 = 25$

Lastly, combine any terms that allow this (usually, but not always, the two middle terms):

35x+10x = 45x

Arrange your answer in descending exponential form, and you're done.

(7x+5)(2x+5) = 14x^2 + 45x +25

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Example Question #51 : Foil

Distribute and simplify: (ax+by)(ax+by)

Possible Answers:

a^2x^2 + b^2y^2+2abxy

a^2x^2 + b^2y^2+a^2b^2x^2y^2

a^2x^2 + b^2y^2+abxy^2

ax^2 + by^2+abxy^2

Correct answer:

a^2x^2 + b^2y^2+2abxy

Explanation:

To FOIL this binomial distribution, we simply distribute the terms in a specific order:

(ax+by)(ax+by)

Multiply the First terms:

$ax\cdot ax = a^2x^2$

Multiply the Outer terms:

$ax\cdot by = abxy$

Multiply the Inner terms:

$by\cdot ax = abxy$

Multiply the Last terms:

$by\cdot by = b^2y^2$

Lastly, combine any terms that allow this (usually, but not always, the two middle terms):

abxy+abxy = 2abxy

Arrange your answer in descending exponential form, and you're done.

(ax+by)(ax+by) = a^2x^2 + b^2y^2+2abxy

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Example Question #57 : How To Use Foil With The Distributive Property

Distribute and simplify: (x-4)(x+7)

Possible Answers:

x^2+3x-28

x^2+3x+28

x^2-3x-28

x^2-3x+28

Correct answer:

x^2+3x-28

Explanation:

To FOIL this binomial distribution, we simply distribute the terms in a specific order:

(x-4)(x+7)

Multiply the First terms:

$x\cdot x = x^2$

Multiply the Outer terms:

$x\cdot 7 = 7x$

Multiply the Inner terms:

$-4\cdot x = -4x$

Multiply the Last terms:

$-4\cdot 7 = -28$

Lastly, combine any terms that allow this (usually, but not always, the two middle terms):

7x-4x = 3x

Arrange your answer in descending exponential form, and you're done.

(x-4)(x+7) = x^2+3x-28

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Example Question #58 : How To Use Foil With The Distributive Property

Distribute and simplify: (2a^3+ 4x^2)(-b^3 - 5y^2)

Possible Answers:

-2a^6b^6 - 10ay^5 - 4b^3x^2 - 20x^2y^2

2a^3b^3 - 10a^3y^2 + 4b^3x^2 - 20x^2y^2

-2a^3b^3 - 10a^3y^2 - 4b^3x^2 - 20x^2y^2

-3a^3b^3 - 7a^3y^2 - 5b^3x^2 - 9x^2y^2

Correct answer:

-2a^3b^3 - 10a^3y^2 - 4b^3x^2 - 20x^2y^2

Explanation:

The trick to this expression is to remember that only those terms which share both common variables AND common exponents are additive. In other words, you cannot add a^3 + b^3 any more than you can add $b^3 + b^{300}$ .

To FOIL this binomial distribution, we simply distribute the terms in a specific order:

(2a^3+ 4x^2)(-b^3 - 5y^2)

Multiply the First terms:

$2a^3\cdot -b^3 = -2a^3b^3$

Multiply the Outer terms:

$2a^3\cdot -5y^2 = -10a^3y^2$

Multiply the Inner terms:

$4x^2\cdot -b^3 = -4b^3x^2$

Multiply the Last terms:

$4x^2\cdot -5y^2 = -20x^2y^2$

Lastly, combine any terms that allow this (usually, but not always, the two middle terms). In this case, no two terms are compatible.

Arrange your answer in descending exponential form, and you're done.

(2a^3+ 4x^2)(-b^3 - 5y^2) = -2a^3b^3 - 10a^3y^2 - 4b^3x^2 - 20x^2y^2

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Example Question #51 : Distributive Property

The expression (2x+4)(9-x) is equivalent to:

Possible Answers:

2x^2-14x-36

2x^2+14x+36

x^2+14x+36

-2x^2+22x+36

-2x^2+14x+36

Correct answer:

-2x^2+14x+36

Explanation:

Use the grid method to FOIL.

Foil

Combine the like terms.

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Example Question #1 : How To Use The Grid Method For Foil

Which of the following is the product of (3a^3+6)(a^3-5) ?

Possible Answers:

3a^6+9a^3-30

3a^6-9a^3-30

3a^6+21a^3-30

3a^6-30

3a^6-21^3-30

Correct answer:

3a^6-9a^3-30

Explanation:

Using FOIL which stands for the multiplication process between the Firsts, Outers, Inners, and Lasts, we end up with the expression

3a^6-15a^3+6a^3-30 .

From there, combine the like terms -15a^3+6a^3 to get -9a^3 .

Therefore the product becomes,

3a^6-9a^3-30

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ACT Math : Distributive Property

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #2632 : Act Math

Example Question #52 : How To Use Foil With The Distributive Property

Example Question #53 : How To Use Foil With The Distributive Property

Example Question #54 : How To Use Foil With The Distributive Property

Example Question #55 : How To Use Foil With The Distributive Property

Example Question #51 : Foil

Example Question #57 : How To Use Foil With The Distributive Property

Example Question #58 : How To Use Foil With The Distributive Property

Example Question #51 : Distributive Property

Example Question #1 : How To Use The Grid Method For Foil

All ACT Math Resources

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