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Question

Evaluate the following products without multiplying directly:
(i) 100 × 107
(ii) 95 × 96
(iii) 104 × 96

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Solution

(i) 103×107=(100+3)(100+7)
=(100)2+(3+7)×100+3×7
=10000+1000+21=11021

(ii) 95×96=(1005)(1004)
=(100)2(5+4)×100+5×4
=10000900+20=9120

(iii) Using identity: (a+b)(ab)=a2b2
104×96
=(100+4)(1004)
=(100242)
=1000016=9984

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