# Algebra II : Multiplication and Division

## Example Questions

### Example Question #1 : Multiplication And Division

Let x and y be complex numbers

Evaluate the product .

Explanation:

### Example Question #2 : Multiplication And Division

Solve for  if .

None of the other answers.

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 .

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 #1 : Multiplication And Division

Find the Prime Factorization of .

Explanation:

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

### Example Question #1 : Multiplication And Division

Using the distributive property, simplify the following:

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 #1 : Multiplication And Division

Simplify the following:

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 #1 : Multiplication And Division

Multiply:

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 #1 : Multiplication And Division

What is ?

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 #2 : Multiplication And Division

What is ?

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

What is ?