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Question

Using suitable identity find the value of 104×96.

A
9962
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B
9974
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C
9984
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D
9998
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Solution

The correct option is C 9984
Concept Involved––––––––––––––––––:
(m+n)×(mn)
Using the FOIL rule.
=m×(mn)+n×(mn)
=m2mn+nm+n2
=m2+mnnm+n2
We know mnnm=0
=m2n2

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

104×96=(100+4)×(1004)
(100+4)×(1004)=100×(1004)+4×(1004)
=10021004+410042
=1002+1004410042
We know 10044100=0
=100242
=10,00016
=9984

This is the required expression obtained using FOIL rule.
Also, we can use the identity
(m+n)(mn)=m2n2.

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