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प्रश्न
Evaluate using algebraic formula:
983 + 6(98)2 + 12(98) + 23
मूल्यांकन
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उत्तर
983 + 6(98)2 + 12(98) + 23
Let’s rewrite the expression in a recognizable identity form,
(a + b)3 = a3 + 3a2b + 3ab2 + b3
Here, let a = 98, b = 2,
Now, expanding (98 + 2)3 = 1003
(98 + 2)3 = (98)3 + 3(98)2(2) + 3(98)(2)2 + (2)3
= (98)3 + 6(98)2 + 3(98)(4) + (2)3
= (98)3 + 6(98)2 + 12(98) + (2)3
= (100)3
∴ (98 + 2)3 = 10,00,000
Hence, 983 + 6(98)2 + 12(98) + 23 = (100)3 = 10,00,000
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