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Question

Using (x+a)(x+b)=x2+(a+b)x+ab, find
(i) 103×104
(ii) 5.1×5.2
(iii) 103×98
(iv) 9.7×9.8

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Solution

i) 103×104=(100+3)(100+4)
=(100)2+(3+4)100+(3)(4)
=10000+700+12
=10712

ii) 5.1×5.2=(5+0.1)(5+0.2)
=(5)2+(0.1+0.2)5+(0.1)(0.2)
=25+1.5+0.02
=26.52

iii) 103×98=(100+3)(1002)
=(100)2+(32)100+(3)(2)
=10000+1006
=10094

iv) 9.7×9.8=(9+0.7)(9+0.8)
=(9)2+(0.7+0.8)9+(0.7)(0.8)
=81+13.5+0.56
=95.06

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