The identity used in simplifying 103 x 97
The identity used in simplifying 103 x 97
A) (a + b)2 = a2 + 2ab + b2
B) (a – b)2 = a2 – 2ab + b2
C) (a – b) (a + b) = a2 – b2
D) (x + a) (x + b) = x2 + (a + b) x + ab
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Correct option is (C) (a – b) (a + b) = a2 – b2
\(103\times97\) = (100 + 3) (100 - 3)
Let a = 100, b = 3
Then \(103\times97\) \(=(a+b)(a-b)\) \(=a^2-b^2\)
\(=100^2-3^2\)
= 10000 - 9 = 9991
\(\therefore\) Identity that is used in simplifying \(103\times97\) is \((a-b)(a+b)=a^2-b^2.\)
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