Question

PLEASE HELP. Prove that the value of the expression: b (36^5−6^9)(38^9−38^8) is divisible by 30 and 37.

Answer 1

Answer:

Step-by-step explanation:

First factor the second binomial

38^9 - 38^8 = 38^9 (38 - 1 ) = 38^9(37)

So there's your 37. This whole expression is divisible by 37

Now do the first  binomial

36^5 - (36^4)*6

36^4(36 - 6)

36^4(30) and there's your thirty.

That first term is going to cause a bit of trouble showing that 36^4 * 6 = 6^9

6(36^4) = 6(6^2)^4 = 6^1 * 6^8 = 6^9

So this factors into 30*(36^4)*37*38^9