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

(30) (37) (-6⁷) (38⁸)

Step-by-step explanation:

(36⁴-6⁹) (38⁹-38⁸)

(36⁴ - 6⁹) = (6²) ⁴ - 6⁹

= 6⁸ - 6⁹

= 6⁷ (6 - 6²)

= 6⁷ (6 - 36)

= 6⁷ (-30)

(38⁹ - 38⁸)

= 38⁸ (38 - 1)

= 38⁸ (37)

36⁴-6⁹) (38⁹-38⁸)

6⁷ (-30) * 38⁸ (37)

(30) (37) (-6⁷) (38⁸)

Clearly 30 and 37 are factors, so divisible by them