Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.

Factor out the GCF 7^6

7^8 - 7^7 + 7^6 = 7^6(7^2 - 7^1 + 7^0)

7^8 - 7^7 + 7^6 = 7^6(49 - 7 + 1)

7^8 - 7^7 + 7^6 = 7^6(42 + 1)

7^8 - 7^7 + 7^6 = 7^6*43

The term 43 is part of the final factorization after fully simplifying. We don't need to find the value of 7^6. This is enough to prove that the original expression is divisible by 43.

i'm pretty sure it's 477,585,296, but perhaps my math is incorrect.