Question

What polynomial identity will prove that 117=125-8

Answer 1

Difference of cubes polynomial identity prove that 117 =125-8

Explanation:

Difference of cubes:- A polynomial in the form of
`a^3 -b^3` is called the difference of cubes.

The formula for difference of cubes is;

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

To prove: 117 = 125 - 8

Take RHS

`125-8 = 5^3 -2^3`

Apply difference of cubes;

`5^3-2^3 = (5-2)(5^2+2^2+5\cdot 2)`

=
`3(25+4+10) = 3(39) = 117` = LHS hence proved!

Therefore, difference of cubes polynomial identity will prove that 117 = 125-8