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 = 38^8 (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

(6^2)^5 - 6^9

6^10 - 6^9  

6^9(6 - 1)

6^9 *5           Take out one of the 6s

6^8 * 6 * 5

6^8 * 30

So the first factor is divisible by 30

and the second factor is divisible by 37

So this factors into 30*6^8*37*38^9