Mathematics
Using (a + b)2 = (a2 + b2 + 2ab), evaluate:
(i) (137)2
(ii) (1008)2
(iii) (11.6)2
Expansions
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Answer
(i) Given,
⇒ (137)2
⇒ (130 + 7)2
Using identity :
(a + b)2 = a2 + b2 + 2ab
⇒ (130 + 7)2 = (130)2 + 72 + 2 × 130 × 7
⇒ (130 + 7)2 = 16900 + 49 + 1820 = 18769.
Hence, (137)2 = 18769.
(ii) Given,
⇒ (1008)2
⇒ (1000 + 8)2
Using identity :
(a + b)2 = a2 + b2 + 2ab
⇒ (1000 + 8)2 = (1000)2 + 82 + 2 × 1000 × 8
⇒ (1000 + 8)2 = 1000000 + 64 + 16000 = 1016064.
Hence, (1008)2 = 1016064.
(iii) Given,
⇒ (11.6)2
⇒ (11 + 0.6)2
Using identity :
(a + b)2 = a2 + b2 + 2ab
⇒ (11 + 0.6)2 = (11)2 + (0.6)2 + 2 × 11 × 0.6
⇒ (11 + 0.6)2 = 121 + 0.36 + 13.2 = 134.56
Hence, (11.6)2 = 134.56.
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