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Question

Evaluate the following:

(i) 102×106        (ii) 109×107        (iii) 35×37        (iv) 53×55

(v) 103×96         (vi) 34×36           (vii) 994×1006


Solution

(i) 102×106=(100+2)(100+6)=(100)2+(2+6)×100+2×6=10000+800+12=10812(ii) 109×107=(100+9)(100+7)=(100)2+(9+7)×100+9×7=10000+1600+63=11663(iii) 35×37=(30+5)(30+7)=(30)2+(5+7)×30+5×7=900+12×30+35=900+360+35=1295(iv) 53×55=(50+3)(50+5)=(50)2+(3+5)×50+3×5=2500+8×50+15=2500+400+15=2915(v) 103×96=(100+3)(1004)=(100)2+(34)×100+3×(4)=10000+(1)×10012=1000010012=10000112=9888(vi) 34×36=(30+4)(30+6)=(30)2+(4+6)×30+4×6=900+10×30+24=900+300+24=1224(vii) 994×1006=(10006)(1000+6)=(1000)2+(6+6)×1000+(6)×6=1000000+036=100000036=999964


Mathematics
RD Sharma
Standard VIII

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