Answer:
Difference of cubes polynomial identity prove that 117 =125-8
Step-by-step explanation:
Difference of cubes:- A polynomial in the form of [tex]a^3 -b^3[/tex] is called the difference of cubes.
The formula for difference of cubes is;
[tex]a^3 -b^3 = (a-b)(a^2+b^2+ab)[/tex]
To prove: 117 = 125 - 8
Take RHS
[tex]125-8 = 5^3 -2^3[/tex]
Apply difference of cubes;
[tex]5^3-2^3 = (5-2)(5^2+2^2+5\cdot 2)[/tex]
=[tex]3(25+4+10) = 3(39) = 117[/tex] = LHS hence proved!
Therefore, difference of cubes polynomial identity will prove that 117 = 125-8
