Sum and Difference of Cubes - Algebra II
Card 0 of 32
Which of the following is equivalent to 
?
Which of the following is equivalent to 
Whenever you see the sum of two cubes, as you do here since 
and 
, you can factor that sum using the formula:
Here that allows you to replace 
with 
and 
with 
to get:
Whenever you see the sum of two cubes, as you do here since 
Here that allows you to replace 
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Factor 
.
Factor 
The key to solving this problem is noticing that there is something special about 8, 
, and 216; they are all cubes of different values (2, x, and 6). Therefore, we can apply the Sum of Cubes formula, which is:
In our case, a=2x and b=6. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
The key to solving this problem is noticing that there is something special about 8, 
In our case, a=2x and b=6. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
Compare your answer with the correct one above
Factor 
.
Factor 
The key to solving this problem is noticing that there is something special about 
; they are all cubes of different values (5, x, 3). Therefore, we can apply the Sum of Cubes formula, which is:
In our case, a=5x and b=3. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
The key to solving this problem is noticing that there is something special about 
In our case, a=5x and b=3. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
Compare your answer with the correct one above
Factor 
Factor
The key to solving this problem is noticing that there is something special about 8, 
, and 64; they are all cubes of different values (2, a, and 4). Therefore, we can apply the Difference of Cubes formula, which is:
In our case, a=2a and b=4. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
The key to solving this problem is noticing that there is something special about 8, 
In our case, a=2a and b=4. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
Compare your answer with the correct one above
Which of the following is equivalent to 
?
Which of the following is equivalent to 
Whenever you see the difference of two cubes - as you do here with 
and 
, which is 
, you can apply the formula for Difference of Cubes to factor that term:
Here that means you can follow the template with 
and 
to get:
Whenever you see the difference of two cubes - as you do here with 
Here that means you can follow the template with 
Compare your answer with the correct one above
Which of the following is equivalent to 
?
Which of the following is equivalent to 
This problem has you go backward from a notable rule, the Sum of Cubes rule. You should recognize the Sum of Cubes as 
. Here you should see the familiar symptoms of that rule: in the rightmost set of parentheses, you have two squared terms, 
and 
, and you have their square roots (
and 
) in the leftmost set. Once you've determined that you're dealing with the Sum of Cubes structure, the conversion should be relatively quick without having to distribute the multiplication manually.
This problem has you go backward from a notable rule, the Sum of Cubes rule. You should recognize the Sum of Cubes as 
Compare your answer with the correct one above
Which of the following is equivalent to 
?
Which of the following is equivalent to 
This problem employs the Sum of Cubes rule, which states that:
Here you should see that the given expression, 
, can be written as a sum of two cubes: 
. This allows you to invoke the formula, resulting in:
This problem employs the Sum of Cubes rule, which states that:
Here you should see that the given expression, 
Compare your answer with the correct one above
The expression 
is equivalent to:
The expression 
This problem calls on your knowledge of the Difference of Cubes rule, which states that:
Here you're given two parentheticals in this exact form, allowing you to invoke the rule to solve without manually expanding the parentheses through multiplication. Your 
and 
terms are 
and 
, so you can simply express the answer as 
.
This problem calls on your knowledge of the Difference of Cubes rule, which states that:
Here you're given two parentheticals in this exact form, allowing you to invoke the rule to solve without manually expanding the parentheses through multiplication. Your 
Compare your answer with the correct one above
Which of the following is equivalent to ?
Which of the following is equivalent to
Whenever you see the sum of two cubes, as you do here since and , you can factor that sum using the formula:
Here that allows you to replace with and with to get:
Whenever you see the sum of two cubes, as you do here since
Here that allows you to replace
Compare your answer with the correct one above
Factor .
Factor
The key to solving this problem is noticing that there is something special about 8, , and 216; they are all cubes of different values (2, x, and 6). Therefore, we can apply the Sum of Cubes formula, which is:
In our case, a=2x and b=6. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
The key to solving this problem is noticing that there is something special about 8,
In our case, a=2x and b=6. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
Compare your answer with the correct one above
Factor .
Factor
The key to solving this problem is noticing that there is something special about ; they are all cubes of different values (5, x, 3). Therefore, we can apply the Sum of Cubes formula, which is:
In our case, a=5x and b=3. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
The key to solving this problem is noticing that there is something special about
In our case, a=5x and b=3. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
Compare your answer with the correct one above
Factor
Factor
The key to solving this problem is noticing that there is something special about 8, , and 64; they are all cubes of different values (2, a, and 4). Therefore, we can apply the Difference of Cubes formula, which is:
In our case, a=2a and b=4. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
The key to solving this problem is noticing that there is something special about 8,
In our case, a=2a and b=4. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
Compare your answer with the correct one above
Which of the following is equivalent to ?
Which of the following is equivalent to
Whenever you see the difference of two cubes - as you do here with and , which is , you can apply the formula for Difference of Cubes to factor that term:
Here that means you can follow the template with and to get:
Whenever you see the difference of two cubes - as you do here with
Here that means you can follow the template with
Compare your answer with the correct one above
Which of the following is equivalent to ?
Which of the following is equivalent to
This problem has you go backward from a notable rule, the Sum of Cubes rule. You should recognize the Sum of Cubes as . Here you should see the familiar symptoms of that rule: in the rightmost set of parentheses, you have two squared terms, and , and you have their square roots ( and ) in the leftmost set. Once you've determined that you're dealing with the Sum of Cubes structure, the conversion should be relatively quick without having to distribute the multiplication manually.
This problem has you go backward from a notable rule, the Sum of Cubes rule. You should recognize the Sum of Cubes as
Compare your answer with the correct one above
Which of the following is equivalent to ?
Which of the following is equivalent to
This problem employs the Sum of Cubes rule, which states that:
Here you should see that the given expression, , can be written as a sum of two cubes: . This allows you to invoke the formula, resulting in:
This problem employs the Sum of Cubes rule, which states that:
Here you should see that the given expression,
Compare your answer with the correct one above
The expression is equivalent to:
The expression
This problem calls on your knowledge of the Difference of Cubes rule, which states that:
Here you're given two parentheticals in this exact form, allowing you to invoke the rule to solve without manually expanding the parentheses through multiplication. Your and terms are and , so you can simply express the answer as .
This problem calls on your knowledge of the Difference of Cubes rule, which states that:
Here you're given two parentheticals in this exact form, allowing you to invoke the rule to solve without manually expanding the parentheses through multiplication. Your
Compare your answer with the correct one above
Factor .
Factor
The key to solving this problem is noticing that there is something special about 8, , and 216; they are all cubes of different values (2, x, and 6). Therefore, we can apply the Sum of Cubes formula, which is:
In our case, a=2x and b=6. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
The key to solving this problem is noticing that there is something special about 8,
In our case, a=2x and b=6. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
Compare your answer with the correct one above
Factor .
Factor
The key to solving this problem is noticing that there is something special about ; they are all cubes of different values (5, x, 3). Therefore, we can apply the Sum of Cubes formula, which is:
In our case, a=5x and b=3. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
The key to solving this problem is noticing that there is something special about
In our case, a=5x and b=3. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
Compare your answer with the correct one above
Factor
Factor
The key to solving this problem is noticing that there is something special about 8, , and 64; they are all cubes of different values (2, a, and 4). Therefore, we can apply the Difference of Cubes formula, which is:
In our case, a=2a and b=4. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
The key to solving this problem is noticing that there is something special about 8,
In our case, a=2a and b=4. Plugging this in, we get
Because this is factored, our work here is done! Teachers often encourage students to use the acronym "SOAP" to help them solve Sum and Difference of Cubes problems. The acronym SOAP refers to the signs in the expanded/factored form. The first one is always the Same as in the original equation, the second one is always Opposite the original sign, and the final one is Always Positive no matter. Same, Opposite, Always Positive = SOAP.
Compare your answer with the correct one above
Which of the following is equivalent to ?
Which of the following is equivalent to
Whenever you see the difference of two cubes - as you do here with and , which is , you can apply the formula for Difference of Cubes to factor that term:
Here that means you can follow the template with and to get:
Whenever you see the difference of two cubes - as you do here with
Here that means you can follow the template with
Compare your answer with the correct one above