Mathematics
Use the formula: (a + b) (a - b) = a2 - b2 to evaluate:
(i) 21 x 19
(ii) 33 x 27
(iii) 103 x 97
(iv) 9.8 x 10.2
(v) 7.7 x 8.3
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Answer
(i) 21 x 19
(20 + 1)(20 - 1)
Using the formula: (a + b) (a - b) = a2 - b2
⇒ (20 + 1)(20 - 1) = 202 - 12
= 400 - 1
= 399
Hence, 21 x 19 = 399.
(ii) 33 x 27
(30 + 3)(30 - 3)
Using the formula: (a + b) (a - b) = a2 - b2
⇒ (30 + 3)(30 - 3) = 302 - 32
= 900 - 9
= 891
Hence, 33 x 27 = 891.
(iii) 103 x 97
(100 + 3)(100 - 3)
Using the formula: (a + b) (a - b) = a2 - b2
⇒ (100 + 3)(100 - 3) = 1002 - 32
= 10000 - 9
= 9991
Hence, 103 x 97 = 9991.
(iv) 9.8 x 10.2
(10 - 0.2)(10 + 0.2)
Using the formula: (a + b) (a - b) = a2 - b2
⇒ (10 - 0.2)(10 + 0.2) = 102 - (0.2)2
= 100 - 0.04
= 99.96
Hence, 9.8 x 10.2 = 99.96.
(v) 7.7 x 8.3
(8 - 0.3)(8 + 0.3)
Using the formula: (a + b) (a - b) = a2 - b2
⇒ (8 - 0.3)(8 + 0.3) = 82 - (0.3)2
= 64 - 0.09
= 63.91
Hence, 7.7 x 8.3 = 63.91.
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