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Which expression is a difference of cubes?
X^6-6
X^6-8
x^8-6
X^8-8


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.

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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.