question_answer 1)

                Using \[(x+a)(x+b)\,={{x}^{2}}+(a+b)\]\[x+ab,\] find                 (i) \[103\times 104\]                       (ii) \[5.1\times 5.2\]                        (iii) \[103\times 98\]                       (iv) \[9.7\times 9.8\]

Answer:

                (i) \[103\times 104\]                                       \[103\times 104\,=(100+3)\times (100+4)\] \[={{(100)}^{2}}+(3+4)(100)+(3)(4)\] \[=10000+700+12\] \[=10712\] (ii) \[5.1\times 5.2\] \[5.1\times .5.2=(5+0.1)\times (5+0.2)\] \[=\,{{(5)}^{2}}+(0.1+0.2)\,(5)\,+(0.1)\,(0.2)\] \[=25+1.5+0.02\] = 26.52                 (iii) \[103\times 98\]                       \[103\times 98=(100+3)\times (100-2)\] \[=(100+3)\,\{(100+(-2)\}\] \[={{(100)}^{2}}+\{3+(-2)\,\}\,(100+(3)\,(-2)\] = 10000 + 100 ? 6 = 10094 (iv) \[9.7\times 9.8\] \[9.7\times 9.8=(10-0.3)\,(10-0.2)\] \[={{(10)}^{2}}-(0.3+0.2)\,(10)+(0.3)\,(0.2)\] = 100 ? 5 + 0.06 = 95.06.