Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Ask your questions and receive precise answers from experienced professionals across different disciplines. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Answer: The correct expression is, [tex]x^6-8[/tex]
Step-by-step explanation:
[tex]x^6[/tex] is represented in cube form as, [tex](x^2)^3[/tex]
'8' is represented in cube form as, [tex]2^3[/tex]
[tex]x^8[/tex] and '6' will not show cube form of integer power.
The expanded form of the given expression, [tex]x^6-8[/tex] is represented as,
[tex]x^6-8=(x^2)^3-2^3[/tex]
This expression will showing the difference of cubes.
And the other options, [tex]x^6-6,x^8-6,x^8-8[/tex] will not show the difference of cubes.
Therefore, the correct answer is, [tex]x^6-8[/tex]
The expression [tex]\boxed{{x^6} - 8}[/tex] is a difference of cubes. Option (b) is correct.
Further Explanation:
The cubic formula can be expressed as follows,
[tex]\boxed{{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)}[/tex]
Given:
The options are as follows,
(a). [tex]{x^6} - 6[/tex]
(b). [tex]{x^6} - 8[/tex]
(c). [tex]{x^8} - 6[/tex]
(d). [tex]{x^8} - 8[/tex]
Calculation:
8 is a cube of 2 and can be written as follows,
[tex]8 = {2^3}[/tex]
[tex]{x^6}[/tex] can be written as a cube of [tex]{x^2}.[/tex]
[tex]{x^6} = {\left( {{x^2}} \right)^3}[/tex]
Use the identity [tex]{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)[/tex] in above expression.
[tex]\begin{aligned}{x^6} - 8&= {\left( {{x^2}} \right)^3}- {\left( 2 \right)^3} \\&= \left( {{x^2} - 2} \right)\left( {{x^4} + 2{x^2} + 4} \right)\\\end{aligned}[/tex]
The expression [tex]\boxed{{x^6} - 8}[/tex] is a difference of cubes. Option (b) is correct.
Option (a) is not correct.
Option (b) is correct.
Option (c) is not correct.
Option (d) is not correct.
Learn more:
1. Learn more about unit conversion https://brainly.com/question/4837736
2. Learn more about non-collinear https://brainly.com/question/4165000
3. Learn more aboutbinomial and trinomial https://brainly.com/question/1394854
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Exponents and Powers
Keywords: Solution, factorized form, [tex]x^12y^18+1[/tex], exponents, power, equation, power rule, exponent rule.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
