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

Question

Jaydon Herring

Mathematics

18 December, 02:22

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

+4

Answers (1)

Know the Answer?

Karma Mills · Answer 1

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.