Prove that for any natural n: the number 3^(n + 2) −2^(n +2) +3^n −2^n is divisible by 10.

Let us manipulate this expression:     by algebraically manipulating, we are not changing the value of this expression.exponent property:     we use that exponent property to decompose those exponents.        move  together with  to set up for factoring by grouping.    factor out  out of the left section    factor out  out of the right section            factor out 10 from the entire thing:         exponent property:       apply:     so a series of manipulations tells is that the above result is equal to the original expression.if we divide  by 10, the 10 factor will cancel out. the entirety of the inside is just a natural number since exponents raised to a natural number results in a natural number answer.so it's divisible by 10.