GED Math : Quadratic Equations

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #74 : How To Use Foil In The Distributive Property

Which terms do the following expressions share when simplified?

 

Possible Answers:

 only

 and 

 and 

 and 

 and 

Correct answer:

 only

Explanation:

 is a special type of factorization.

When simplified, the "middle terms" cancel out, because they are the same value with opposite signs:

Expressions in the form  always simplify to  

At this point, we know that the only possible answers are q2 and -81.

However, now we have to check the terms of the second expression to see if we find any similarities.

 

Here we notice that rather than cancelling out, the middle terms combine instead of cancel. Also, our final term is the product of two negative numbers, and so is positive. Comparing the two simpified expressions, we find that only  is shared between them.

 

Example Question #4940 : Algebra 1

Use the distributive property (use FOIL method) to solve the following

Possible Answers:

Correct answer:

Explanation:

Remember that FOIL stands for First, Outer, Inner, Last. We will add up the different parts. If we had an expression

than we would have

First: 

Outer: 

Inner: 

Last: 

Foil

For this problem we have

First: 

Outer: 

Inner: 

Last: 

Adding these together gives

check: let's add the first two numbers and multiply that by the sum of the last two,

Example Question #133 : Distributive Property

Simplify the following using the distributive property of FOIL:

Possible Answers:

Correct answer:

Explanation:

When using the FOIL method to distribute, we do the following:

FIRST

OUTSIDE

INSIDE

LAST

In other words, we multiply the first terms, the outside terms, the inside terms, and the last terms.

FIRST 

OUTSIDE 

INSIDE 

LAST 

 

Now, we combine all the terms.  We get

We can simplify, and we are left with

Example Question #11 : Foil

Simplify the following using the grid method for FOIL:

Possible Answers:

Correct answer:

Explanation:

To solve using the grid method, we use the given problem

and create a grid using each term.

Foil grid 1

Now, we fill in the boxes by multiplying the terms in each row and column.

Foil grid 2

Now, we write each of the multiplied terms out,

We combine like terms.

Therefore, by using the grid method, we get the solution

Example Question #11 : Foil

Simplify:

Possible Answers:

Correct answer:

Explanation:

All you need to do for this is to FOIL (or, distribute correctly).

First, multiply the first terms:

Next, multiply the last terms:

Now, multiply the inner and outer terms:

Combining all of these, you get:

Example Question #11 : Foil

Simplify:

Possible Answers:

Correct answer:

Explanation:

All you need to do for this is to FOIL (or, distribute correctly).  However, you must be careful because of the  in front of the groups.  Just leave that for the end.  First, FOIL the groups.

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

First, multiply the first terms:

Next, multiply the last terms:

Now, multiply the inner and outer terms:

Combining all of these, you get:

Then, multiply everything by :

Example Question #13 : Foil

Simplify:

Possible Answers:

Correct answer:

Explanation:

You just need to methodically multiply for these kinds of questions.  However, first move around your groups to make your life a bit easier.  Look at the problem this way:

Now, the first pair is a difference of squares, so you can multiply that out quickly!

After this, you are in a FOIL case.

Start by multiplying the first terms:

Then, multiply the final terms:

Then, multiply the inner and outer terms:

Now, combine them all:

Example Question #14 : Foil

Solve:   

Possible Answers:

Correct answer:

Explanation:

Use the FOIL method to solve this expression.

Simplify each term.

Combine like-terms.

The answer is:  

Example Question #15 : Foil

Solve:  

Possible Answers:

Correct answer:

Explanation:

Apply the FOIL method to solve this problem.

Multiply the first term of the first binomial with both terms of the second binomial.

Multiply the second term of the first binomial with both terms of the second binomial.

Add both quantities.

The answer is:  

Example Question #21 : Foil

Solve:  

Possible Answers:

Correct answer:

Explanation:

Use the FOIL method to solve.  Multiply the first term of the first binomial with both terms of the second binomial.

Multiply the second term of the first binomial with both terms of the second binomial.

Add the quantities by combining like-terms.

The answer is:   

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