Answer :
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.
