A) So, \[{{\operatorname{y}}^{4}}-12{{y}^{2}}+ y+14 \,is \,{{y}^{4}}-17{{y}^{3}}-46{{y}^{2}}+ 52y- 54 \,greater than 17{{y}^{3}}+ 34{{y}^{2}}- 51y+ 68.\]
B) So, \[17{{y}^{3}}+ 34{{y}^{2}}- 51y+ 68 \,greater than {{\operatorname{y}}^{4}}-12{{y}^{2}}+ y+14 \,is \,{{y}^{4}}-17{{y}^{3}}-46{{y}^{2}}+ 52y- 54\]
C) All are correct
D) None of these
Correct Answer: A
Solution :
Sol. Required expression is \[89{{a}^{3}}-64{{a}^{2}}+6a+ 16-(21{{a}^{3}}-17{{a}^{2}})\] \[=\,\,\,89{{a}^{3}}-64{{a}^{2}}+6a+16-21{{a}^{3}}+17{{a}^{2}}\] On combining the like terms, \[= 89{{a}^{3}}-21{{a}^{3}}- 64{{a}^{2}}+\,17{{a}^{2}}+ 6a+16\] \[=\,\,68{{a}^{3}}-47{{a}^{2}}+6a+16\] So, \[21{{a}^{3}}-17{{a}^{2}}\,\,is 68{{a}^{3}}-47{{a}^{2}}+6a+16 \,less than \,89{{a}^{3}}- 64{{a}^{2}}+ 6a+16.\]
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