(i) (46)3 + (34)3
= (40 + 6)3 + (40-6)3
= (40)3 + (6)3 + 3 × 40 × 6(40 + 6) + (40)3 – (6)3 – 3 × 40 × 6(40 – 6)
= 2(40)3 + 3 × 40 × 6[46 – 34]
= 2(40)3 + 720 × 12
= 128000 + 8640 = 136640
(ii) (23)3 – (17)3
= (20 + 3)3 – (20 – 3)3
= (20)3 + (3)3 + 3 × 20 × 3(20 + 3) – (20)3 + (3)3 + 3 × 20 × 3(20 – 3)
= 2(3)3 + 3 × 20 × 3(23 + 17)
= 2 × 27 + 180(40) = 54+ 7200 = 7254
(iii) (111)3 – (89)3
= (100 + 11)3 – (100 – 11)3
= (100)3 + (11)3 + 3 × 100 × 11 (100 + 11) – (100)3 + (11)3 + 3 × 100 × 11(100 – 11)
= 2(11)3 + 3 × 100 × 11(111 + 89)
= 2(1331) + 3 × 100 × 11 × 200
= 2662 + 660000 = 662662
