Answer:
option (3) satisfies the products that will result in a difference of cubes.
\((x-9)(x^2+9x+81)=x^3-3^3\)
Step-by-step explanation:
Given : Some options.
We have to choose the products that will result in a sum or difference of cubes.
A sum or difference of cubes is given by:
\(a^3-b^3=(a-b)(a^2+b^2+ab)\)
and \(a^3+b^3=(a+b)(a^2+b^2-ab)\)
Thus, out of given
\((x-9)(x^2+9x+81)\) is in the same form as \(a^3-b^3\) where a = x and b = 9.
Thus, \((x-9)(x^2+9x+81)=x^3-3^3=x^3-729\)
Thus, only option (3) satisfies the products that will result in a difference of cubes.
