College

We appreciate your visit to Which are sums of perfect cubes Check all that apply A tex 8x 6 27 tex B tex x 9 1 tex C tex 81x. 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!

Which are sums of perfect cubes? Check all that apply.

A. [tex]8x^6 + 27[/tex]
B. [tex]x^9 + 1[/tex]
C. [tex]81x^3 + 16x^6[/tex]
D. [tex]x^6 + x^3[/tex]
E. [tex]27x^9 + x^{12}[/tex]
F. [tex]9x^3 + 27x^9[/tex]

Answer :

Sure! Let's go through each expression and determine which are sums of perfect cubes.

1. Expression: [tex]\(8x^6 + 27\)[/tex]
- [tex]\(8x^6\)[/tex] can be rewritten as [tex]\((2x^2)^3\)[/tex] because [tex]\((2x^2)\)[/tex] cubed is [tex]\(8x^6\)[/tex].
- [tex]\(27\)[/tex] is a cube of [tex]\(3\)[/tex] because [tex]\(3^3 = 27\)[/tex].
- Therefore, [tex]\(8x^6 + 27\)[/tex] can be expressed as a sum of perfect cubes.

2. Expression: [tex]\(x^9 + 1\)[/tex]
- [tex]\(x^9\)[/tex] can be rewritten as [tex]\((x^3)^3\)[/tex] because [tex]\((x^3)\)[/tex] cubed is [tex]\(x^9\)[/tex].
- [tex]\(1\)[/tex] is a cube of [tex]\(1\)[/tex] because [tex]\(1^3 = 1\)[/tex].
- Therefore, [tex]\(x^9 + 1\)[/tex] is a sum of perfect cubes.

3. Expression: [tex]\(81x^3 + 16x^6\)[/tex]
- [tex]\(81x^3\)[/tex] can be rewritten as [tex]\((3x)^3\)[/tex] because [tex]\((3x)\)[/tex] cubed is [tex]\(81x^3\)[/tex].
- [tex]\(16x^6\)[/tex] can be rewritten as [tex]\((2x^2)^3\)[/tex] because [tex]\((2x^2)\)[/tex] cubed is [tex]\(16x^6\)[/tex].
- Therefore, [tex]\(81x^3 + 16x^6\)[/tex] is a sum of perfect cubes.

4. Expression: [tex]\(x^6 + x^3\)[/tex]
- These terms cannot be directly rewritten as a sum of two perfect cubes.
- Therefore, [tex]\(x^6 + x^3\)[/tex] is not a sum of perfect cubes.

5. Expression: [tex]\(27x^9 + x^{12}\)[/tex]
- [tex]\(27x^9\)[/tex] can be rewritten as [tex]\((3x^3)^3\)[/tex] because [tex]\((3x^3)\)[/tex] cubed is [tex]\(27x^9\)[/tex].
- [tex]\(x^{12}\)[/tex] can be rewritten as [tex]\((x^4)^3\)[/tex] because [tex]\((x^4)\)[/tex] cubed is [tex]\(x^{12}\)[/tex].
- Therefore, [tex]\(27x^9 + x^{12}\)[/tex] is a sum of perfect cubes.

6. Expression: [tex]\(9x^3 + 27x^9\)[/tex]
- These terms cannot be directly rewritten as a sum of two perfect cubes.
- Therefore, [tex]\(9x^3 + 27x^9\)[/tex] is not a sum of perfect cubes.

After analyzing each expression, the sums of perfect cubes are:
- [tex]\(8x^6 + 27\)[/tex]
- [tex]\(x^9 + 1\)[/tex]
- [tex]\(81x^3 + 16x^6\)[/tex]
- [tex]\(27x^9 + x^{12}\)[/tex]

Thanks for taking the time to read Which are sums of perfect cubes Check all that apply A tex 8x 6 27 tex B tex x 9 1 tex C tex 81x. 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!

Rewritten by : Barada