ACT Math : How to multiply binomials with the distributive property

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : Binomials And Foil

Which of the following expressions is equivalent to: 6x (m2 +yx2 3)?

 

Possible Answers:

xm2 + 7x3 -18

6xm2 + 7x3 -18

6xm2 + 6yx2 -18x

6xm2 + 6yx3 -18

6xm2 + 6yx3 -18x

Correct answer:

6xm2 + 6yx3 -18x

Explanation:

6x (m2 +yx2 3)= 6x∙m2 + 6xyx2 – 6x∙3= 6xm2 + 6yx3 -18x (Use Distributive Property)

 

 

Example Question #2 : How To Multiply Binomials With The Distributive Property

Which of the following expressions is equivalent to: ?

Possible Answers:

Correct answer:

Explanation:

Use the distributive property to multiply  by all of the terms in :

Example Question #2 : Binomials And Foil

If  and  are constants and  is equivalent to , what is the value of ?

Possible Answers:

Cannot be determined from the given information.

Correct answer:

Explanation:

The question gives us a quadratic expression and its factored form. From this, we know 

At this point, solve for t.

Now, we can plug in  to get

.

Now, use FOIL to get s.

Example Question #3 : Binomials And Foil

Which expression is equal to ?

Possible Answers:

Correct answer:

Explanation:

In this problem, we are to multiply the two binomials using the FOIL method. This method stands for the order in which you multiply the variables. F stands for the first term of each binomial. O stands for the outside terms, meaning the first term of the first binomial and the last term of the second. I stands for the inside terms, meaning the second term of the first binomial and the first term of the second. L stands for the last term of each binomial. Once you do this, you simply add each part together to recieve your polynomial answer. Here is how our problem is solved:

Example Question #4 : Binomials And Foil

Which expression is equal to ?

Possible Answers:

Correct answer:

Explanation:

In this problem, we are to multiply the two binomials using the FOIL method. This method stands for the order in which you multiply the variables. F stands for the first term of each binomial. O stands for the outside terms, meaning the first term of the first binomial and the last term of the second. I stands for the inside terms, meaning the second term of the first binomial and the first term of the second. L stands for the last term of each binomial. Once you do this, you simply add each part together to recieve your polynomial answer. Here is how our problem is solved:

Example Question #5 : Binomials And Foil

Which expression is equal to ?

Possible Answers:

Correct answer:

Explanation:

In this problem, we are to multiply the two binomials using the FOIL method. This method stands for the order in which you multiply the variables. F stands for the first term of each binomial. O stands for the outside terms, meaning the first term of the first binomial and the last term of the second. I stands for the inside terms, meaning the second term of the first binomial and the first term of the second. L stands for the last term of each binomial. Once you do this, you simply add each part together to recieve your polynomial answer. Here is how our problem is solved:

Example Question #6 : Binomials And Foil

Which expression is equal to ?

Possible Answers:

Correct answer:

Explanation:

In this problem, we are to multiply the two binomials using the FOIL method. This method stands for the order in which you multiply the variables. F stands for the first term of each binomial. O stands for the outside terms, meaning the first term of the first binomial and the last term of the second. I stands for the inside terms, meaning the second term of the first binomial and the first term of the second. L stands for the last term of each binomial. Once you do this, you simply add each part together to recieve your polynomial answer. Here is how our problem is solved:

Example Question #7 : Binomials And Foil

Which expression is equal to ?

Possible Answers:

Correct answer:

Explanation:

In this problem, we are to multiply the two binomials using the FOIL method. This method stands for the order in which you multiply the variables. F stands for the first term of each binomial. O stands for the outside terms, meaning the first term of the first binomial and the last term of the second. I stands for the inside terms, meaning the second term of the first binomial and the first term of the second. L stands for the last term of each binomial. Once you do this, you simply add each part together to recieve your polynomial answer. Here is how our problem is solved:

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