Question

Show that:

$\left(i\right){13}^3-5^3$ is divisible by 8.

$\left(ii\right){35}^3+{27}^3$ is divisible by 62.

Answer 1

(i) (13³ - 5³)

[Using identity (a³ - b³) = (a - b)(a² + ab + b²)]

=(13 - 5)(13² + 13 × 5 + 5²)

=8(169 + 65 + 25)

Therefore, the number is divisible by 8.

(ii) (35³ + 27³)

[Using identity (a³ + b³)=(a + b)(a² - ab + b²)]

=(35 + 27)(35² + 35× 27 + 27²)

=62 × (35² + 35 × 27 + 27²)

Therefore, the number is divisible by 62.