Question

Which polynomial expression represents a sum of cubes? (6 – s)(s2 + 6s + 36) (6 + s)(s2 – 6s – 36) (6 + s)(s2 – 6s + 36) (6 + s)(s2 + 6s + 36)

Answer 1

c) (6+s) (s2-6s+36)
For sum of cubes you add the first binomial and subtract then add in the following trinomial.
a3+b3=(a+b)(a2-ab+b2)

Answer 2

Option 3 is correct that is
`(6+s)(s^2-6s+36)`

Explanation:

We have general formula for sum of cube which is

`a^3+b^3=(a+b)(a^2+b^2-ab)`

Here, we have a=s and b=6

on substituting the values in the formula we will get

`6^3+s^3=(6+s)(s^2+6^2-6s)`

After simplification we will get

`6^3+s^3=(6+s)(s^2+36-6s)`

After rearranging the terms we will get

`6^3+s^3=(6+s)(s^2-6s+36)` which exactly matches option 3 in the given options.

Therefore, option 3 is correct that is
`(6+s)(s^2-6s+36)`