EXERCISE 4B
Find the value of each of the following using the short-cut method:
(1) (25)3
Solution: Here, a = 2 and b = 5
| a2 ×a a3 | a2 ×3b 3a2b | b2 ×3a 3ab2 | b2 ×b b3 |
| 4 × 2 8 15 | 4 × 15 60 + 16 76 | 25 × 6 150 +12 162 | 25 × 5 125
|
∴ (25)3 = 15625
(2) (47)3
Solution: Here, a = 4 and b = 7
| a2 ×a a3 | a2 ×3b 3a2b | b2 ×3a 3ab2 | b2 ×b b3 |
| 16 × 4 64 103 | 16 × 21 336 + 62 398 | 49 × 12 588 +34 622 | 49 × 7 343
|
∴ (47)3 = 103823
(3) (68)3
Solution: Here, a = 6 and b = 8
| a2 ×a a3 | a2 ×3b 3a2b | b2 ×3a 3ab2 | b2 ×b b3 |
| 36 × 6 216 314 | 36 × 24 864 + 120 984 | 64 × 18 1152 +51 1203 | 64 × 8 512
|
∴ (68)2 = 314432
(4) (84)3
Solution: here, a = 8 and b = 4
| a2 ×a a3 | a2 ×3b 3a2b | b2 ×3a 3ab2 | b2 ×b b3 |
| 64 × 8 512 592 | 64 × 12 768 + 39 807 | 16 × 24 384 +6 390 | 16 × 4 64
|
∴ (84)3 = 592704
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