x⁶ - 8
Further explanation
Given:
Question:
Which expression is a difference of cubes?
The Process:
The difference of cubes is as follows: [tex]\boxed{ \ a^3 - b^3 \ }[/tex]
Based on this form, from the three options above the answer is the second option.
Because the second option [tex]\boxed{ \ x^6 - 8 \ }[/tex], consist of the first term with an exponent that are divisible by three and the second term with a cubic exponent. Such as the following:
- [tex]\boxed{ \ x^6 = (x^2)^3 \ }[/tex]
- [tex]\boxed{ \ 8 = 2^3 \ }[/tex]
Therefore the answer is [tex]\boxed{\boxed{ \ x^6 - 8 = (x^2)^3 - 2^3 \ }}[/tex], which is a difference of cubes.
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Notes
- The difference of squares is as follows: [tex]\boxed{ \ a^2 - b^2 \ }[/tex]
- Now consider how to describe a difference of squares: [tex]\boxed{ \ a^2 - b^2 = (a + b)(a - b) \ }[/tex]
- Differentiate from the term "square of difference", which is: [tex]\boxed{ \ (a - b)^2 \ } \rightarrow \boxed{ \ a^2 + b^2 - 2ab \ }[/tex]
Learn more
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- 68.32 divided by 2.8 is divisible https://brainly.com/question/5022643
