question_answer 1)

                Using \[{{a}^{2}}-{{b}^{2}}=(a+b)\,(a-b),\] find                 (i) \[{{51}^{2}}-{{49}^{2}}\]                 (ii) \[{{(1.02)}^{2}}-{{(0.98)}^{2}}\]                 (iii) \[{{153}^{2}}-{{147}^{2}}\]                 (iv) \[{{12.1}^{2}}-{{7.9}^{2}}\].

Answer:

                (i) \[{{51}^{2}}-{{49}^{2}}\] \[{{51}^{2}}-{{49}^{2}}=(51+49)\,(51-49)\] \[=(100)\,(2)\] = 200                 (ii) \[{{(1.02)}^{2}}-{{(0.98)}^{2}}\]           \[{{(1.02)}^{2}}-{{(0.98)}^{2}}\] \[=(1.02+0.98)\,(1.02-0.98)\] \[=(2)\,(0.04)\] = 0.08                 (iii) \[{{153}^{2}}-{{147}^{2}}\] \[{{153}^{2}}-{{147}^{2}}=(153+147)\,(153-147)\] \[=(300)\,(6)\] = 1800                 (iv) \[{{12.1}^{2}}-{{7.9}^{2}}\] \[{{12.1}^{2}}-{{7.9}^{2}}\]\[=(12.1+7.9)\,(12.1-7.9)\] = 84