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Question

The value of (102)×(98) is

A
9,992
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B
9,994
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C
9,996
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D
9,998
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Solution

The correct option is C 9,996
Concept Involved––––––––––––––––––:
(a+b)(ab)=a2b2

Method–––––––:
Using the FOIL rule.
F=First terms, O= Outside terms, I = Inside terms, L= Last terms.

(102)×(98)=(100+2)×(1002)
=(100)(100)+(100)(2)+(2)(100)+(2)(2)
=10022(100)+2(100)22
=1002+2(100)2(100)22
=100222
=10,0004
=9,996

This is the required expression obtained using FOIL rule.
Also, we can use the identity
(a+b)(ab)=a2b2.

(102)×(98)=(100+2)×(1002)
=(100+2)(1002)
=100222
=10,0004
=9,996

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