Simplify the following using the rules for identities :
(i) $69^{2} - 59^{2}$
(ii) $101^{2} - 91^{2}$
(iii) $1002^{2} - 998^{2}$

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Solution

As $a^{2} - b^{2} = (a - b) (a + b)$
i) $(69)^{2} - (59)^{2} = (69 - 59) (69 + 59) = (10) (128) = 1280$
Hence the answer $1280$
ii) $(101)^{2} - (91)^{2} = (101 - 91) (101 + 91) = (10) (192) = 1920$
Hence the answer $1920$
iii) $(1002)^{2} - (998)^{2} = (1002 - 998) (1002 + 998) = (4) (2000) = 8000$
Hence the answer $8000$

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