We appreciate your visit to Which are sums of perfect cubes Check all that apply tex 8x 6 27 tex tex x 9 1 tex tex 81x 3 16x 6. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To determine which expressions are sums of perfect cubes, let's analyze each expression one by one. An expression is a sum of perfect cubes if each term can be expressed as the cube of a simpler expression.
1. Expression: [tex]\(8x^6 + 27\)[/tex]
- [tex]\(8x^6\)[/tex] can be written as [tex]\((2x^2)^3\)[/tex], which is a perfect cube.
- [tex]\(27\)[/tex] can be written as [tex]\(3^3\)[/tex], which is also a perfect cube.
- So, [tex]\(8x^6 + 27\)[/tex] is a sum of perfect cubes.
2. Expression: [tex]\(x^9 + 1\)[/tex]
- [tex]\(x^9\)[/tex] can be written as [tex]\((x^3)^3\)[/tex], which is a perfect cube.
- [tex]\(1\)[/tex] can be written as [tex]\(1^3\)[/tex], which is a perfect cube.
- Thus, [tex]\(x^9 + 1\)[/tex] is a sum of perfect cubes.
3. Expression: [tex]\(81x^3 + 16x^6\)[/tex]
- [tex]\(81x^3\)[/tex] does not correspond to a perfect cube.
- However, [tex]\(16x^6\)[/tex] can be written as [tex]\((2x^2)^3\)[/tex], which is a perfect cube.
- Since [tex]\(81x^3\)[/tex] is not a perfect cube, [tex]\(81x^3 + 16x^6\)[/tex] is not a sum of perfect cubes.
4. Expression: [tex]\(x^6 + x^3\)[/tex]
- [tex]\(x^6\)[/tex] can be written as [tex]\((x^2)^3\)[/tex], which is a perfect cube.
- [tex]\(x^3\)[/tex] can be written as [tex]\(x^3\)[/tex], which is also a perfect cube.
- Therefore, [tex]\(x^6 + x^3\)[/tex] is a sum of perfect cubes.
5. Expression: [tex]\(27x^9 + x^{12}\)[/tex]
- [tex]\(27x^9\)[/tex] can be written as [tex]\((3x^3)^3\)[/tex], which is a perfect cube.
- [tex]\(x^{12}\)[/tex] can be written as [tex]\((x^4)^3\)[/tex], which is a perfect cube.
- Consequently, [tex]\(27x^9 + x^{12}\)[/tex] is a sum of perfect cubes.
6. Expression: [tex]\(9x^3 + 27x^9\)[/tex]
- [tex]\(9x^3\)[/tex] does not correspond to a perfect cube.
- [tex]\(27x^9\)[/tex] can be written as [tex]\((3x^3)^3\)[/tex], which is a perfect cube.
- Since [tex]\(9x^3\)[/tex] is not a perfect cube, [tex]\(9x^3 + 27x^9\)[/tex] is not a sum of perfect cubes.
Based on the analysis, the expressions that are sums of perfect cubes are:
- [tex]\(8x^6 + 27\)[/tex]
- [tex]\(x^9 + 1\)[/tex]
- [tex]\(x^6 + x^3\)[/tex]
- [tex]\(27x^9 + x^{12}\)[/tex]
1. Expression: [tex]\(8x^6 + 27\)[/tex]
- [tex]\(8x^6\)[/tex] can be written as [tex]\((2x^2)^3\)[/tex], which is a perfect cube.
- [tex]\(27\)[/tex] can be written as [tex]\(3^3\)[/tex], which is also a perfect cube.
- So, [tex]\(8x^6 + 27\)[/tex] is a sum of perfect cubes.
2. Expression: [tex]\(x^9 + 1\)[/tex]
- [tex]\(x^9\)[/tex] can be written as [tex]\((x^3)^3\)[/tex], which is a perfect cube.
- [tex]\(1\)[/tex] can be written as [tex]\(1^3\)[/tex], which is a perfect cube.
- Thus, [tex]\(x^9 + 1\)[/tex] is a sum of perfect cubes.
3. Expression: [tex]\(81x^3 + 16x^6\)[/tex]
- [tex]\(81x^3\)[/tex] does not correspond to a perfect cube.
- However, [tex]\(16x^6\)[/tex] can be written as [tex]\((2x^2)^3\)[/tex], which is a perfect cube.
- Since [tex]\(81x^3\)[/tex] is not a perfect cube, [tex]\(81x^3 + 16x^6\)[/tex] is not a sum of perfect cubes.
4. Expression: [tex]\(x^6 + x^3\)[/tex]
- [tex]\(x^6\)[/tex] can be written as [tex]\((x^2)^3\)[/tex], which is a perfect cube.
- [tex]\(x^3\)[/tex] can be written as [tex]\(x^3\)[/tex], which is also a perfect cube.
- Therefore, [tex]\(x^6 + x^3\)[/tex] is a sum of perfect cubes.
5. Expression: [tex]\(27x^9 + x^{12}\)[/tex]
- [tex]\(27x^9\)[/tex] can be written as [tex]\((3x^3)^3\)[/tex], which is a perfect cube.
- [tex]\(x^{12}\)[/tex] can be written as [tex]\((x^4)^3\)[/tex], which is a perfect cube.
- Consequently, [tex]\(27x^9 + x^{12}\)[/tex] is a sum of perfect cubes.
6. Expression: [tex]\(9x^3 + 27x^9\)[/tex]
- [tex]\(9x^3\)[/tex] does not correspond to a perfect cube.
- [tex]\(27x^9\)[/tex] can be written as [tex]\((3x^3)^3\)[/tex], which is a perfect cube.
- Since [tex]\(9x^3\)[/tex] is not a perfect cube, [tex]\(9x^3 + 27x^9\)[/tex] is not a sum of perfect cubes.
Based on the analysis, the expressions that are sums of perfect cubes are:
- [tex]\(8x^6 + 27\)[/tex]
- [tex]\(x^9 + 1\)[/tex]
- [tex]\(x^6 + x^3\)[/tex]
- [tex]\(27x^9 + x^{12}\)[/tex]
Thanks for taking the time to read Which are sums of perfect cubes Check all that apply tex 8x 6 27 tex tex x 9 1 tex tex 81x 3 16x 6. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
