Respuesta :
Answer:
a) x^6-27
Step-by-step explanation:
Since we can write the expresion as :
((x^2)^3)-(3^3)
which is effectively a diffrence of cubes
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.
[tex]\begin{array}{l}{\text { a) } x^{6}-27} \\\\ {=x^{2 x}-3^{3}} \\\\ {\text { using law of exponent } a^{m \times n}=\left(a^{m}\right)^{n}} \\\\ {=\left(x^{2}\right)^{3}-(3)^{3}}\end{array}[/tex]
[tex]\text { so a ) that is } x^{6}-27 \text { is difference of cube of } x^{2} \text { and cube of } 3[/tex]
[tex]\begin{array}{l}{\text { b) } x^{15}-36} \\\\ {=x^{5 \times 3}-6^{2}} \\\\ {=\left(x^{5}\right)^{3}-(6)^{2}}\end{array}[/tex]
[tex]\text { so b) that is } x^{15}-36 \text { is difference of cube of } x^{2} \text { and square of } 6[/tex]
[tex]\begin{array}{l}{\text { c) } x^{16}-64} \\\\ {=x^{8 \times 2}-4^{3}} \\\\ {=\left(x^{8}\right)^{2}-(4)^{3}}\end{array}[/tex]
[tex]\text { so c) that is } x^{16}-64 \text { is difference of square of } x^{8} \text { and cube of } 4[/tex]
[tex]\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}[/tex]
Hence we can clearly conclude that expression a) that is x^6- 27 is only difference of cubes out of the given expression.
