Operations in Expressions - Basic Math
Card 0 of 80
Factor the following expression completely:
Factor the following expression completely:
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To factor an expression in the form 
, we need to find factors of 
that add up to 
.
In this case, 
and 
.
Start by listing factors of 24 and adding them up. You want the one that adds up to 10.
Because 4 and 6 are the factors that we need, you can then write
To check if you factored correctly, you can multiply the two factors together. If you end up with the original expression, then you are correct.
To factor an expression in the form
In this case,
Start by listing factors of 24 and adding them up. You want the one that adds up to 10.
Because 4 and 6 are the factors that we need, you can then write
To check if you factored correctly, you can multiply the two factors together. If you end up with the original expression, then you are correct.
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This question requires you to understand order of operations, which is represented by the acronym "PEMDAS": parentheses, exponents, multiplication and division, addition and subtraction.
Solve the expression within the parenthesis first, beginning with multiplication:
The next operation in the order of operations is division.
Finally, use addition to solve the equation:
This question requires you to understand order of operations, which is represented by the acronym "PEMDAS": parentheses, exponents, multiplication and division, addition and subtraction.
Solve the expression within the parenthesis first, beginning with multiplication:
The next operation in the order of operations is division.
Finally, use addition to solve the equation:
Factor the following expression completely
Factor the following expression completely
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First, we need to factor the numerator and the denominator separately.
To factor an expression with the form 
, we will need to find factors of 
that add up to be.
For the numerator, 
, 
and 
.
Write down the factors of 
and add them up.
Since 
and 
add up to 
, 
Now, do the same thing with the denominator, 
.
Since 
and 
add up to 
, 
.
Now, stack these factors up as fractions:
Since both the numerator and denominator have the factors (x+6), they cancel each other out because they divide to 1.
Then,
First, we need to factor the numerator and the denominator separately.
To factor an expression with the form
For the numerator,
Write down the factors of
Since
Now, do the same thing with the denominator,
Since
Now, stack these factors up as fractions:
Since both the numerator and denominator have the factors (x+6), they cancel each other out because they divide to 1.
Then,
Factor the following expression: 
Factor the following expression:
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When you factor an expression, you are separating it into its basic parts. When you multiply those parts back together, you should obtain the original expression.
The first step when factoring an expression is to see if all of the terms have something in common. In this case, 
, 
, and 
all have an 
which can be taken out:
The next step is to focus on what's in the parentheses. To factor an expression of form 
, we want to try to find factors 
, where 
and 
. We therefore need to look at the factors of 
to see if we can find two that add to 
:
We've found our factors! We can therefore factor what's inside the parentheses, 
, as 
. If we remember the 
we factored out to begin with, our final completely factored answer is:
When you factor an expression, you are separating it into its basic parts. When you multiply those parts back together, you should obtain the original expression.
The first step when factoring an expression is to see if all of the terms have something in common. In this case,
The next step is to focus on what's in the parentheses. To factor an expression of form
We've found our factors! We can therefore factor what's inside the parentheses,
What is 
?
What is
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When terms with the same base are multiplied, multiply the coefficients together then add up all the exponents.
For the coefficients: 
For the exponents: 
Thus, the answer is 
When terms with the same base are multiplied, multiply the coefficients together then add up all the exponents.
For the coefficients:
For the exponents:
Thus, the answer is
Factor 
Factor
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To factor an equation in the form 
, where 
and 
, you must find factors of 
that add up to 
.
List the factors of 36 and add them together:
Since 
, 
is the factor we need. Plug this factor in to get the final answer.
To factor an equation in the form
List the factors of 36 and add them together:
Since
Simplify:
Simplify:
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When dividing terms with the same bases, remember to subtract the exponents.
Keep in mind that when there is a negative exponent in the numerator, putting that term in the denominator will make the exponent positive.
When dividing terms with the same bases, remember to subtract the exponents.
Keep in mind that when there is a negative exponent in the numerator, putting that term in the denominator will make the exponent positive.
Evaluate
Evaluate
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We first need to apply the Exponent Rule to our two terms.
and
.
Then we do subtraction to obtain our final answer,
.
We first need to apply the Exponent Rule to our two terms.
Then we do subtraction to obtain our final answer,
Which of the following is equivalent to 
?
Which of the following is equivalent to
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Since all of the answer choices look like 
, let's find 
in 
.
Then,
When you have an exponent being raised to an exponent, multiply the exponents together.
Since all of the answer choices look like
Then,
When you have an exponent being raised to an exponent, multiply the exponents together.
Simplify the following expression:
Simplify the following expression:
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The correct answer is 
due to the law of exponents. When solving this type of problem, it is easiest to focus on like terms (i.e. terms containing x or terms containing y).
First we can start by simplifying the 'x' terms. We start with 
which is equivalent to 
. We then are left with 
.
Now we can simplify the 'y' terms as follows: 
.
Last, the 'z' terms can be simplified as follows: 
.
This leaves us with the final simplified answer of 
.
The correct answer is
First we can start by simplifying the 'x' terms. We start with
Now we can simplify the 'y' terms as follows:
Last, the 'z' terms can be simplified as follows:
This leaves us with the final simplified answer of
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Start by simplifying the numerator.
When an exponent is raised to another exponent, multiply the two exponents together.
Now, tackle the denominator. When two numbers of the same base are multiplied, you want to add the exponents.
Put the numerator and denominator together:
When you have a fraction with terms that have the same base, you want to subtract the exponent in the denominator from the exponent in the numerator.
To make a term with a negative exponent in the numerator positive, put it in the denominator.
Start by simplifying the numerator.
When an exponent is raised to another exponent, multiply the two exponents together.
Now, tackle the denominator. When two numbers of the same base are multiplied, you want to add the exponents.
Put the numerator and denominator together:
When you have a fraction with terms that have the same base, you want to subtract the exponent in the denominator from the exponent in the numerator.
To make a term with a negative exponent in the numerator positive, put it in the denominator.
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This is a classic order of operations question, and if you are not careful, you can end up with the wrong answer!
Remember, the order of operations says that you have to go in the following order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (also known as PEMDAS). In this equation, you will start with the parentheses. In the parentheses, we have
.
But within the parentheses, you still need to follow PEMDAS. First, we will solve the exponent, and the square of 2 is 4. Then, we'll divide 16 by 4, which gives us 4, so we can rewrite our original equation as
.
We can now divide 
into 
, which gives us
.
The last step is to add and subtract the numbers above, paying careful attention to negative signs. In the end, we end up with 
because 
added to 
equals 
, and 
minus 
equals 
.
This is a classic order of operations question, and if you are not careful, you can end up with the wrong answer!
Remember, the order of operations says that you have to go in the following order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (also known as PEMDAS). In this equation, you will start with the parentheses. In the parentheses, we have
But within the parentheses, you still need to follow PEMDAS. First, we will solve the exponent, and the square of 2 is 4. Then, we'll divide 16 by 4, which gives us 4, so we can rewrite our original equation as
We can now divide
The last step is to add and subtract the numbers above, paying careful attention to negative signs. In the end, we end up with
Solve:
Solve:
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Use the order of operations: PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).
We want to solve what's in the parentheses first.
Now, do the division and the multiplication.
Therefore our equation becomes:
Finally, subtract.
Use the order of operations: PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).
We want to solve what's in the parentheses first.
Now, do the division and the multiplication.
Therefore our equation becomes:
Finally, subtract.
Solve:
Solve:
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Use order of operations, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to solve.
Since there are no parentheses or exponents we can go straight to multiplication and division.
and 
Therefore the following happens:
Then add and subtract.
Use order of operations, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to solve.
Since there are no parentheses or exponents we can go straight to multiplication and division.
Therefore the following happens:
Then add and subtract.
Simplify
Simplify
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We start with what is inside the parentheses, so 
becomes 
.
Next, we take care of any exponents, giving us 
.
Next, we take care of multiplication/division, giving us 
or 
.
Finally, we carry out our addition/subtraction, leaving us with 
.
We start with what is inside the parentheses, so
Next, we take care of any exponents, giving us
Next, we take care of multiplication/division, giving us
Finally, we carry out our addition/subtraction, leaving us with
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Using order of operations, we need to solve whatever is in the parentheses first.
Next, do the multiplication and division.
Finally, add and subtract.
Using order of operations, we need to solve whatever is in the parentheses first.
Next, do the multiplication and division.
Finally, add and subtract.
Solve:
Solve:
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Using PEMDAS, we do the parenthetical bit first:
Now, we do multiplication and division:
Finally, subtract.
Using PEMDAS, we do the parenthetical bit first:
Now, we do multiplication and division:
Finally, subtract.
When evaluating the expression
,
which of the five operations must be carried out third?
When evaluating the expression
which of the five operations must be carried out third?
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By the order of operations, any operations within parentheses must be carried out first; there are two here, the addition and the subtraction. After this is done, the exponent, or squaring, must be worked before the other operations. Squaring, the third operation, is therefore the correct answer.
By the order of operations, any operations within parentheses must be carried out first; there are two here, the addition and the subtraction. After this is done, the exponent, or squaring, must be worked before the other operations. Squaring, the third operation, is therefore the correct answer.
When evaluating the expression
,
in which order must you work the three operations?
When evaluating the expression
in which order must you work the three operations?
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By the order of operations, in the absence of grouping symbols, multplication must be worked before adding or subtracting. Then the addition and subtraction must be worked in left-to-right order; the subtraction is at left, so the subtraction is worked next, followed by the addition.
By the order of operations, in the absence of grouping symbols, multplication must be worked before adding or subtracting. Then the addition and subtraction must be worked in left-to-right order; the subtraction is at left, so the subtraction is worked next, followed by the addition.
When evaluating the expression
,
in which order must you work the three operations?
When evaluating the expression
in which order must you work the three operations?
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By the order of operations, in the absence of grouping symbols, the exponent (represented here by cubing) must be worked first. The multiplication must be worked second, followed by the subtraction.
By the order of operations, in the absence of grouping symbols, the exponent (represented here by cubing) must be worked first. The multiplication must be worked second, followed by the subtraction.