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ACT Math : Exponents and the Distributive Property

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Example Questions

Example Question #81 : Exponents

Distribute and simplify: (x^2-1)(x+8)

Possible Answers:

x^3 +7x^2 - 8

10x^2 - x - 8

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

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

Correct answer:

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

Explanation:

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

(x^2-1)(x+8)

Multiply the First terms:

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

Multiply the Outer terms:

$x^2\cdot 8 = 8x^2$

Multiply the Inner terms:

$-1\cdot x = -x$

Multiply the Last terms:

$-1\cdot 8 = -8$

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.

(x^2-1)(x+8) = x^3 +8x^2 - x - 8

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Example Question #82 : Exponents

Distribute and simplify: (5x^2-x)(2x+1)

Possible Answers:

10x^3 + 7x^2 - x

10x^3 + 2x^2 + x

10x^3 + 3x^2 - x

10x^2 + 3x + 1

10x^3 - 3x^2 + x

Correct answer:

10x^3 + 3x^2 - x

Explanation:

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

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

Multiply the First terms:

$5x^2\cdot 2x = 10x^3$

Multiply the Outer terms:

$5x^2\cdot 1 = 5x^2$

Multiply the Inner terms:

$-x\cdot 2x = -2x^2$

Multiply the Last terms:

$-x\cdot 1 = -x$

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

5x^2-2x^2 = 3x^2

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

(5x^2-x)(2x+1) = 10x^3 + 3x^2 - x

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Example Question #83 : Exponents

Distribute and simplify: (x^2+x)(x^2+x)

Possible Answers:

x^4+2x^3+x^2

2x^2+2x+x

2x^4+2x^3+x^2

x^4+2x^3+2x^2

x^4+x^3+x^2+x

Correct answer:

x^4+2x^3+x^2

Explanation:

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

(x^2+x)(x^2+x)

Multiply the First terms:

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

Multiply the Outer terms:

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

Multiply the Inner terms:

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

Multiply the Last terms:

$x\cdot x = x^2$

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

x^3+x^3 = 2x^3

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

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

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Example Question #84 : Exponents

Distribute and simplify: (4x^5-4x)(4x^5+4x)

Possible Answers:

$16x^{10} + 16x^2$

$16x^{10} +16x^6 - 16x^2$

$8x^{10} + 8x^2$

$8x^{10} - 8x^2$

$16x^{10} - 16x^2$

Correct answer:

$16x^{10} - 16x^2$

Explanation:

A clever eye might spot that this binomial takes the form (a+b)(a-b) , which means you can jump straight to a^2-b^2 as the answer. But let's look at it in detail below.

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

(4x^5-4x)(4x^5+4x)

Multiply the First terms:

$4x^5\cdot 4x^5 = 16x^{10}$

Multiply the Outer terms:

$4x^5\cdot 4x = 16x^6$

Multiply the Inner terms:

$-4x\cdot 4x^5 = -16x^6$

Multiply the Last terms:

$-4x\cdot 4x = -16x^2$

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

16x^6-16x^6 = 0

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

$(4x^5-4x)(4x^5+4x) = 16x^{10} - 16x^2$

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Example Question #85 : Exponents

Distribute and simplify: (2x^4-2x^3)(6x+3x^7)

Possible Answers:

$6x^{11} - 6x^{10} +12x^5 - 12x^4$

$12x^{25} + 6x^{18} - 4x^{10} - 12x^4$

$7x^5 - 4x^{11} + x^{10} - 2x^5$

$6x^{11} - 6x^{10} +12x^5 - 12x^4$

Correct answer:

$6x^{11} - 6x^{10} +12x^5 - 12x^4$

Explanation:

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

(2x^4-2x^3)(6x+3x^7)

Multiply the First terms:

$2x^4\cdot 6x = 12x^5$

Multiply the Outer terms:

$2x^4\cdot 3x^7 = 6x^{11}$

Multiply the Inner terms:

$-2x^3\cdot 6x = -12x^4$

Multiply the Last terms:

$-2x^3\cdot 3x^7 = -6x^{10}$

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.

$(2x^4-2x^3)(6x+3x^7) = 6x^{11} - 6x^{10} +12x^5 - 12x^4$

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ACT Math : Exponents and the Distributive Property

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #81 : Exponents

Example Question #82 : Exponents

Example Question #83 : Exponents

Example Question #84 : Exponents

Example Question #85 : Exponents

All ACT Math Resources

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