Question

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

Answer 1

The answer is Sum of cubes :)

Answer 2

Answer:

Difference of cubes.

Step-by-step 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:  

$5^3-2^3=(5-2)(5^2+5\times 2+2^2)$

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

$117=(3)(39)$

$117=117$  

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.