Question

Prove that the value of the expression
(16^3–8^3)(4^3 +2^3) is divisible by 63.

Answer 1

Explanation:

16^3 - 8^3

Take out 8^3 as a common factor.

16^3 = 2^3 * 8^3

8^3(2^3 - 1)

8^3(8 - 1) = 8^3 * 7

(4^3 + 2^3) Expand

64 + 8 Combine

72

72 = 9 * 8

Conclusion

(8*3 * 7 )(9*8)

7*9 = 63

So any number containing 63 will divide into the reduced form of

(16^3–8^3)(4^3 +2^3)