Algebra II : Multiplication and Division

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1 : Multiplication And Division

Let x and y be complex numbers

Evaluate the product .

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : Multiplication And Division

Solve for  if .

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

The most important part of this problem is to remember the order of operations: PEMDAS

First: Perform any calculations that are within parentheses.

Second: Perform any calculations that are raised to an exponent.

Third: Working from left to right, perform any multiplications or divisions.

Fourth: Working from left to right, perform any additions or subtractions

 

For this problem:

First we do all of the calculations inside parentheses:   and .

Therefore, the expression becomes .Now working from left to right, we perform any multiplications and/or divisions:  and .

Therefore, the expression becomes  and we simply add the remaining numbers to get 

Example Question #3 : Multiplication And Division

Solve for  if .

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we simply follow our order of operations, PEMDAS:

 

First: Perform any calculations that are within parentheses.

Second: Perform any calculations that are raised to an exponent.

Third: Working from left to right, perform any multiplications or divisions.

Fourth: Working from left to right, perform any additions or subtractions.

 First, we evaluate our parentheses:  and .

The original expression then becomes .

Example Question #4 : Multiplication And Division

Find the Prime Factorization of .

Possible Answers:

Correct answer:

Explanation:

To find the prime factorization of 40, write 40 as a combination of its prime factors.

Example Question #271 : Polynomials

Using the distributive property, simplify the following:

Possible Answers:

Correct answer:

Explanation:

The distributive property is handy to help get rid of parentheses in expressions. The distributive property says you "distribute" the multiple to every term inside the parentheses. In symbols, the rule states that 

So, using this rule, we get 

 

Thus we have our answer is .

Example Question #5 : Multiplication And Division

Simplify the following: 

 

Possible Answers:

Correct answer:

Explanation:

We are dividing the polynomial by a monomial. In essence, we are dividing each term of the polynomial by the monomial. First I like to re-write this expression as a fraction. So,

So now we see the three terms to be divided on top. We will divide each term by the monomial on the bottom. To show this better, we can rewrite the equation. 

 

Now we must remember the rule for dividing variable exponents. The rule is So, we can use this rule and apply it to our expression above. Then,

 

 

Example Question #6 : Multiplication And Division

Multiply: 

Possible Answers:

Correct answer:

Explanation:

The first two factors are the product of the sum and the difference of the same two terms, so we can use the difference of squares:

Now use the FOIL method:

Example Question #7 : Multiplication And Division

What is ?

Possible Answers:

Correct answer:

Explanation:

When dividing, focus on the first digit in the dividend with the divisor.  can go into  only one time. So put the  on top of the  and the  goes under the . Then, take the difference which is . Then bring down the next digit in the dividend which is . Next, figure out if  goes into  which is  times  is  which means we get a difference of zero and so  divides evenly with  to give us a final answer of 

Example Question #2311 : Mathematical Relationships And Basic Graphs

What is ?

Possible Answers:

Correct answer:

Explanation:

When multiplying, you can draw out a grid.

Have three rows and five columns and these should create little boxes.

Count them up individually and you should get 

Example Question #9 : Multiplication And Division

What is ?

Possible Answers:

Correct answer:

Explanation:

When dividing, you draw out  circles.

Then circle  circles and that would be one set.

Once most or all the circles are covered, count out the sets.

There should be 

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