Question

Which is a difference of cubes?

a) x^6-27
b) x^15-36
c) x^16-64
d) x^5-125

Answer 1

a) x^6-27

Explanation:

Since we can write the expresion as :

((x^2)^3)-(3^3)

which is effectively a diffrence of cubes

Answer 2

Option A

Expression a) that is x^6- 27 is only difference of cubes out of the given expression.

Solution:

Need to find which of the expression from given four expression represents difference of cube

Let’s try to represent each term of each given expression in cubic form.

`\begin{array}{l}{\text { a) } x^(6)-27} \\\\ {=x^(2 x)-3^(3)} \\\\ {\text { using law of exponent } a^(m * n)=\left(a^(m)\right)^(n)} \\\\ {=\left(x^(2)\right)^(3)-(3)^(3)}\end{array}`

`\text { so a ) that is } x^(6)-27 \text { is difference of cube of } x^(2) \text { and cube of } 3`

`\begin{array}{l}{\text { b) } x^(15)-36} \\\\ {=x^(5 * 3)-6^(2)} \\\\ {=\left(x^(5)\right)^(3)-(6)^(2)}\end{array}`

`\text { so b) that is } x^(15)-36 \text { is difference of cube of } x^(2) \text { and square of } 6`

`\begin{array}{l}{\text { c) } x^(16)-64} \\\\ {=x^(8 * 2)-4^(3)} \\\\ {=\left(x^(8)\right)^(2)-(4)^(3)}\end{array}`

`\text { so c) that is } x^(16)-64 \text { is difference of square of } x^(8) \text { and cube of } 4`

`\begin{array}{l}{\text { d) } x^(5)-125} \\\\ {=x^(5)-5^(5)} \\\\ {\text { so d) that is } x^(5)-125 \text { is difference of fifth power of } x \text { and fifth power of } 5 .}\end{array}`

Hence we can clearly conclude that expression a) that is x^6- 27 is only difference of cubes out of the given expression.