Multiplication and Division - Algebra II
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Simplify the following: 
Simplify the following:
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,
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
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Using the distributive property, simplify the following:
Using the distributive property, simplify the following:
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 
.
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
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Multiply: 
Multiply:
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:
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:
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Let x and y be complex numbers
Evaluate the product 
.
Let x and y be complex numbers
Evaluate the product
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Find the Prime Factorization of 
.
Find the Prime Factorization of
To find the prime factorization of 40, write 40 as a combination of its prime factors.
To find the prime factorization of 40, write 40 as a combination of its prime factors.
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Solve for 
if 
.
Solve for
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 
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:
Therefore, the expression becomes
Therefore, the expression becomes
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Solve for 
if 
.
Solve for
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 
.
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:
The original expression then becomes
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This question is testing your knowledge of the order of operations.
Do the multiplication/division parts of the question first, then addition/subtraction (in this case, only subtraction).
This question is testing your knowledge of the order of operations.
Do the multiplication/division parts of the question first, then addition/subtraction (in this case, only subtraction).
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What is 
?
What is
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 
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
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What is 
?
What is
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 
.
When dividing, you draw out
Then circle
Once most or all the circles are covered, count out the sets.
There should be
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What is 
?
What is
When multiplying with more than a single digit, focus on the ones digiit before the tens digit. 
is 
. The 
is written down but the 
is carried over to the tens digit. Then we multiply 
and 
which is 
but with the 
that was carried over, we add it to the 
which makes 
. Final answer is 
.
When multiplying with more than a single digit, focus on the ones digiit before the tens digit.
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What is 
?
What is
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 
.
When dividing, focus on the first digit in the dividend with the divisor.
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What is 
?
What is
Remember PEMDAS, the acronym which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. This is the order of operations we need to adhere to.
Multiplication comes before addition.
So multiply out 
and 
which is 
.
Then finally add that with 
to get the final answer of 
.
Remember PEMDAS, the acronym which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. This is the order of operations we need to adhere to.
Multiplication comes before addition.
So multiply out
Then finally add that with
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What is 
What is
Remember PEMDAS, the acronym that stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. This is the order of operations we need to adhere to when doing any arithmetic.
Division comes before subtraction.
So divide out 
and 
which is 
.
Then, subtract that with 
to get the final answer of 
.
Remember PEMDAS, the acronym that stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. This is the order of operations we need to adhere to when doing any arithmetic.
Division comes before subtraction.
So divide out
Then, subtract that with
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What is 
?
What is
Remember PEMDAS, the acronym that stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. This is the order of operations we need to adhere to when doing any arithmetic.
The parentheses go first so do what's inside the parentheses.
The sum of 
and 
is 
.
Then we multiply that with 
to get the final answer of 
Remember PEMDAS, the acronym that stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. This is the order of operations we need to adhere to when doing any arithmetic.
The parentheses go first so do what's inside the parentheses.
The sum of
Then we multiply that with
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Solve:
Solve:
To simply 
, notice that there are variables that can be cancelled out.
Another option is to multiply through the numerator and the denominator, and then reduce.
Remember when their are exponents in the numerator and denominator with the same base you subtract the denominator from the numerator.
To simply
Another option is to multiply through the numerator and the denominator, and then reduce.
Remember when their are exponents in the numerator and denominator with the same base you subtract the denominator from the numerator.
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Solve 
.
Solve
Following the order of operations, let's do all the parenthesis first. Within the parenthesis, we still follow the order of operations, and complete the exponential before doing the addition:
Now we can go through and do all the multiplication and division. Remember, we can't divide through the addition signs, so we'll leave that for later.
Now we can do the addition/subtraction:
Because we're dealing with fractions, it would help if we simplified:
Following the order of operations, let's do all the parenthesis first. Within the parenthesis, we still follow the order of operations, and complete the exponential before doing the addition:
Now we can go through and do all the multiplication and division. Remember, we can't divide through the addition signs, so we'll leave that for later.
Now we can do the addition/subtraction:
Because we're dealing with fractions, it would help if we simplified:
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Multiply the numbers: 
Multiply the numbers:
Multiply the first number with the ones digit of the second number.
Multiply the first number with the tens digit of the second number.
Add a zero to this number.
Add this number with the first number calculated.
The answer is: 
Multiply the first number with the ones digit of the second number.
Multiply the first number with the tens digit of the second number.
Add a zero to this number.
Add this number with the first number calculated.
The answer is:
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Multiply: 
Multiply:
Multiply the first number with the first digit of the second number.
Multiply the first number with the second digit of the second number, and then add a zero to the end of that number.
The number becomes:
Multiply the first number with the hundreds digit of the second number, and then add two zeros to the end of that number.
The number becomes:
Add the three numbers obtained.
The answer is: 
Multiply the first number with the first digit of the second number.
Multiply the first number with the second digit of the second number, and then add a zero to the end of that number.
The number becomes:
Multiply the first number with the hundreds digit of the second number, and then add two zeros to the end of that number.
The number becomes:
Add the three numbers obtained.
The answer is:
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Multiply: 
Multiply:
Multiply the first number with the ones digit of the second number.
Multiply the first number with the tens digit of the second number, and then add a zero to the end of the number.
Add both numbers.
The answer is: 
Multiply the first number with the ones digit of the second number.
Multiply the first number with the tens digit of the second number, and then add a zero to the end of the number.
Add both numbers.
The answer is:
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