Question

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:

(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