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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) Here, we will use the identity x+ax+b=x2+a+bx+ab
102×106=100+2100+6=1002+2+6100+2×6=10000+800+12=10812

(ii) Here, we will use the identity x+ax+b=x2+a+bx+ab
109 × 107=100+9100+7=1002+9+7100+9×7=10000+1600+63=11663

(iii) Here, we will use the identity x+ax+b=x2+a+bx+ab
35 × 37=30+530+7=302+5+730+5×7=900+360+35=1295

(iv) Here, we will use the identity x+ax+b=x2+a+bx+ab
53 × 55=50+350+5=502+3+550+3×5=2500+400+15=2915

(v) Here, we will use the identity x+ax-b=x2+a-bx-ab
103 × 96=100+3100-4=1002+3-4100-3×4=10000-100-12=9888

(vi) Here, we will use the identity x+ax+b=x2+a+bx+ab
34 × 36=30+430+6=302+4+630+4×6=900+300+24=1224

(vii) Here, we will use the identity x-ax+b=x2+b-ax-ab
994 × 1006=1000-6×1000+6=10002+6-6×1000-6×6=1000000-36=999964

Mathematics
RD Sharma (2019, 2020)
All

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