Question

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

Answer 1

Answer: The correct expression is, $x^6-8$

Step-by-step explanation:

$x^6$ is represented in cube form as, $(x^2)^3$

'8' is represented in cube form as, $2^3$

$x^8$ and '6' will not show cube form of integer power.

The expanded form of the given expression, $x^6-8$ is represented as,

$x^6-8=(x^2)^3-2^3$

This expression will showing the difference of cubes.

And the other options, $x^6-6,x^8-6,x^8-8$ will not show the difference of cubes.

Therefore, the correct answer is, $x^6-8$

Answer 2

The expression $\boxed{{x^6} - 8}$ is a difference of cubes. Option (b) is correct.

Further Explanation:

The cubic formula can be expressed as follows,

$\boxed{{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)}$

Given:

The options are as follows,

(a). ${x^6} - 6$

(b). ${x^6} - 8$

(c). ${x^8} - 6$

(d). ${x^8} - 8$

Calculation:

8 is a cube of 2 and can be written as follows,

$8 = {2^3}$

${x^6}$ can be written as a cube of ${x^2}.$

${x^6} = {\left( {{x^2}} \right)^3}$

Use the identity ${a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)$ in above expression.

$\begin{aligned}{x^6} - 8&= {\left( {{x^2}} \right)^3}- {\left( 2 \right)^3} \\&= \left( {{x^2} - 2} \right)\left( {{x^4} + 2{x^2} + 4} \right)\\\end{aligned}$

The expression $\boxed{{x^6} - 8}$ 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 brainly.com/question/4837736

2. Learn more about non-collinear brainly.com/question/4165000

3. Learn more aboutbinomial and trinomial brainly.com/question/1394854

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Exponents and Powers

Keywords: Solution, factorized form, $x^12y^18+1$, exponents, power, equation, power rule, exponent rule.