ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #2631 : Act Math

What is ?

Possible Answers:

Correct answer:

Explanation:

The simple formula for difference of two squares is:

.  

To see this, you can also FOIL out

 

Multiplying the first terms, outer terms, inner terms, and last terms results in the following.

Gathering like terms the x's cancel out.

Example Question #47 : Foil

What is ?

Possible Answers:

Correct answer:

Explanation:

Diffference of two squares formula,

 Note that , negative cancels out.  

You can also FOIL: 

Multiplying the first terms, outer terms, inner terms, and last terms results in the following.

Example Question #1141 : Algebra

Multiply the complex numbers:

 (3+4i)(2+8i).

Possible Answers:

-24+30i

-26-32i

22+32i

-26+32i

26+32i

Correct answer:

-26+32i

Explanation:

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.

Example Question #1142 : Algebra

Solve for .

Possible Answers:

Correct answer:

Explanation:

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. 

Example Question #1143 : Algebra

Possible Answers:

Correct answer:

Explanation:

FOIL by using the distributive property.

Now, simplify.

Example Question #1144 : Algebra

Distribute:

Possible Answers:

Correct answer:

Explanation:

FOIL using the distributive property.

Simplify. 

Example Question #52 : Foil

Distribute and simplify: 

Possible Answers:

Correct answer:

Explanation:

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

Multiply the First terms:

 

Multiply the Outer terms:

Multiply the Inner terms:

Multiply the Last terms:

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

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

Example Question #53 : Distributive Property

What is the simplified form of ?

Possible Answers:

Correct answer:

Explanation:

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

Multiply the First terms:

Multiply the Outer terms:

Multiply the Inner terms:

Multiply the Last terms:

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

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

Notice that this answer is also a difference of squares.

Example Question #54 : Distributive Property

Distribute and simplify: 

Possible Answers:

Correct answer:

Explanation:

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

Multiply the First terms:

 

Multiply the Outer terms:

Multiply the Inner terms:

Multiply the Last terms:

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

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

 

Example Question #55 : Distributive Property

Distribute and simplify: 

Possible Answers:

Correct answer:

Explanation:

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

Multiply the First terms:

 

Multiply the Outer terms:

Multiply the Inner terms:

Multiply the Last terms:

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

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

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