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

Difference of cubes.

Step-by-step explanation:

We are asked to find the identify that will prove that .

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

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

Difference of cubes:

Let us prove that 117=125-8.

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

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.

-2

7 - 9 = -2

reversed:

-2 + 9 = 7