Question

What divides 117^3 + 116^3 - 112^3 - 111^3 Answer With Explanation to recieve brainliest

A)17
B)31
C)5
D)41

Answer 1

Answer:

$\huge{\boxed{\rm{\red{Option=C}}}}$

Step-by-step explanation:

Given that:-

117³+116³-112³-111³

It can be written as

=>(117³-112³)+(116²-111³)

It is in the form of a³-b³

a³-b³=(a-b)(a²+ab+b²)

=>[(117-112)(117²+(117)(112)+112²)]

+[(116-111)(116²+(116)(111)+111²)]

=>(5)[117²+(117)(112)+112²)

+(5)[116²+(116)(111)+111²]

=>5}[117²+(117)(112)+112²]+[116²+(116)(111)+111²]}

So clearly above numerical expression is

the multiple of 5

So 5 divides the given number.