A) \[= -20ab + 3{{b}^{2}}+ 3{{a}^{2}}= 3{{a}^{2}}+ 3{{b}^{2}}-20ab\]
B) \[= -20ab + 3{{b}^{2}}+ 3{{a}^{2}}= 3{{a}^{2}}+ 3{{b}^{2}}-30ab\]
C) All of these
D) None of these
Correct Answer: A
Solution :
Sol. Sum of \[12ab\,-10{{b}^{2}}-18{{a}^{2}}\,\,and \,9ab + 12{{b}^{2}}+14{{a}^{2}}\] \[= \,12ab\,-10{{b}^{2}}-18{{a}^{2}}+ 9ab+12{{b}^{2}}+ 14{{a}^{2}}\] On combining the like terms, \[=\,\,12ab+9ab-10{{b}^{2}}+12{{b}^{2}}-18{{a}^{2}}+14{{a}^{2}}\] \[=\,\,\,21ab+2{{b}^{2}}-4{{a}^{2}}\] Sum of \[\operatorname{ab} + 2{{b}^{2}}\,\,and \,3{{b}^{2}}- {{a}^{2}}\] \[=\,\,\,ab+2{{b}^{2}}+3{{b}^{2}}-{{a}^{2}}\] \[=\,\,\,ab+5{{b}^{2}}-{{a}^{2}}\] Now, subtracting \[21ab + 2{{b}^{2}}- 4{{a}^{2}}\,\,from ab + 5{{b}^{2}}-{{a}^{2}},\] we get \[=\, \left( ab + 5{{b}^{2}}- {{a}^{2}} \right) - \left( 21ab + 2{{b}^{2}}- 4{{a}^{2}} \right)\] \[= \,ab + 5{{b}^{2}}- {{a}^{2}}-21ab -2{{b}^{2}}+ 4{{a}^{2}}\] On combining the like terms, \[= \,ab - 21ab + 5{{b}^{2}}- 2{{b}^{2}}- {{a}^{2}}+ 4{{a}^{2}}\] \[= -20ab + 3{{b}^{2}}+ 3{{a}^{2}}= 3{{a}^{2}}+ 3{{b}^{2}}-20ab\]
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