Question

Which polynomial identity will prove that 117 = 125 − 8?

Answer 1

The answer is Sum of cubes :)

Answer 2

Difference of cubes.

Explanation:

We are asked to find the identify that will prove that
`117=125-8`.

Polynomial identities are equations that are true and have general applications in our algebra work.

We can see that 125 equals
`5^3` and 8 equals
`2^3`. So polynomial identity used in our given problem is difference of cubes.

Difference of cubes:
`a^3-b^3=(a-b)(a^2+ab+b^2)`

Let us prove that 117=125-8.

We can write right hand side of our given equation as:

`5^3-2^3=(5-2)(5^2+5* 2+2^2)`

`125-8=(3)(25+10+4)`

`117=(3)(39)`

`117=117`

We can see that left hand side of our equation is equal to right hand side of equation. Hence, proved that difference of cubes will prove our equation equal.