Respuesta :
Answer:
Option 3)
[tex]x^3-9^3 = (x-9)(x^2 + 9x + 81)[/tex]
Step-by-step explanation:
We use the identities:
[tex]a^3 + b^3 = (a+b)(a^2-ab+b^2)\\a^3-b^3 = (a-b)(a^2+ab+b^2)[/tex]
1.
[tex](x + 7)(x^2 -7x + 14)[/tex]
It is not a sum or difference of cubes because it does not satisfies the identity.
2.
[tex](x + 8)(x^2 + 8x + 64)[/tex]
It is not a sum or difference of cubes because it does not satisfies the identity.
3.
[tex](x - 9)(x^2 + 9x + 81)\\\text{Comparing with the identity:} \\a^3-b^3 = (a-b)(a^2+ab+b^2)\\\text{We get}\\a = x\\b = 9\\x^3-9^3 = (x-9)(x^2 + 9x + 81)[/tex]
Thus, it can be expressed as a difference of cubes.
4.
[tex](x - 10)(x^2 - 10x + 100)[/tex]
It is not a sum or difference of cubes because it does not satisfies the identity.
