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ACT Math : Distributive Property

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Example Questions

Example Question #21 : How To Use Foil With The Distributive Property

Find the product of the two binomials:
(2x-4)(x+8)

Possible Answers:

14x-32

2x^2 + 12x +4

2x^2+12x-32

-2x^2 + 4x +12

x^2+14x-32

Correct answer:

2x^2+12x-32

Explanation:

Use FOIL (First Outside Inside Last) to multiply the binomials:

2x*x = 2x^2

2x*8 = 16x

-4*x = -4x

-4*8 = -32

now combine like terms and you get the result: 2x^2+12x-32

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Example Question #22 : How To Use Foil With The Distributive Property

Expand the following: $\textup{(x+5)(x+3)}$

Possible Answers:

$\textup{8x}$

$\textup{2x}+8$

$\textup{2x}^{2}+15$

$\textup{x}^{2}+\textup{8x}+15$

$\textup{x}^{2}+15$

Correct answer:

$\textup{x}^{2}+\textup{8x}+15$

Explanation:

To reach the solution, use the FOIL method of the distributive property. This stands for First, Outer, Inner, Last. In this particular problem, we begin by multiplying the first two $\textup{x's}$ together, yielding ${\textup{x}}^{2}$ . Then, we multiply $\textup{x}$ by the outer number, which is , yielding $\textup{3x}$ . Next, we multiply the two inner numbers, and $\textup{x}$ , yielding $\textup{5x}$ . Finally, we multiply the last two numbers, and , yielding . Thus, when we add all those together, the answer is $\textup{x}^{2}+\textup{8x}+15$ .

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Example Question #21 : Foil

Distribute: (x+2)(x-3)

Possible Answers:

$x^{2}-x-6$

2x-6

x^2-6

x-6

Correct answer:

$x^{2}-x-6$

Explanation:

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

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

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Example Question #22 : Foil

Distribute: $(6x-2)^{2}$

Possible Answers:

36x^2+24x+4

36x^2-24x+4

36x^2+4

12x^2-24x+4

Correct answer:

36x^2-24x+4

Explanation:

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

(6x-2)^2=36x^2-12x-12x+4=36x^2-24x+4

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Example Question #23 : Foil

Distribute:

(3x+4)^2

Possible Answers:

9x^2-24x+16

9x^2+24x+16

9x^2+16

6x+8

Correct answer:

9x^2+24x+16

Explanation:

FOIL using the distributive property:

(3x+4)(3x+4)=9x^2+12x+12x+16=9x^2+24x+16

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Example Question #24 : Foil

Distribute:

(3x+5)(x+2)

Possible Answers:

3x^2+10

3x^2+11x-10

3x+10

3x^2+11x+10

Correct answer:

3x^2+11x+10

Explanation:

FOIL using the distributive property:

(3x+5)(x+2)=3x^2+6x+5x+10=3x^2+11x+10

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Example Question #25 : Foil

Distribute:

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

Possible Answers:

4x^2+16x+16

4x^2+16

4x^2+8

$4x^{2}+8x+16$

Correct answer:

4x^2+16x+16

Explanation:

FOIL using the distributive property.

(2x+4)^2=4x^2+8x+8x+16=4x^2+16x+16

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Example Question #26 : Foil

Distribute:

$(x^{2}-3)^{2}$

Possible Answers:

x^4+6x^2+9

x^4+9

x^4-6x^2+9

x^4+6x^2-9

Correct answer:

x^4-6x^2+9

Explanation:

FOIL using the distributive property.

x^4-3x^2-3x^2+9=x^4-6x^2+9

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Example Question #27 : Foil

Distribute:

(2x+3)(x^2-4)

Possible Answers:

2x^3+3x^2-8x+12

2x^3-3x^2-8x-12

2x^3+3x^2-8x-12

2x^3+3x^2+8x-12

Correct answer:

2x^3+3x^2-8x-12

Explanation:

FOIL using the distributive property.

2x^3-8x+3x^2-12=2x^3+3x^2-8x-12

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Example Question #28 : Foil

Distribute:

(x-1)(2x+7)

Possible Answers:

2x^2+5x+7

2x^2-5x-7

-2x^2+5x-7

2x^2+5x-7

Correct answer:

2x^2+5x-7

Explanation:

Use the distributive property to FOIL

2x^2+7x-2x-7

Simplify.

2x^2+5x-7

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ACT Math : Distributive Property

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #21 : How To Use Foil With The Distributive Property

Example Question #22 : How To Use Foil With The Distributive Property

Example Question #21 : Foil

Example Question #22 : Foil

Example Question #23 : Foil

Example Question #24 : Foil

Example Question #25 : Foil

Example Question #26 : Foil

Example Question #27 : Foil

Example Question #28 : Foil

All ACT Math Resources

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