A) \[9{{a}^{2}}+4{{b}^{2}}+25{{c}^{2}}-12\,ab-20\,bc+30\,ac\]
B) \[9{{a}^{2}}-4{{b}^{2}}-5{{c}^{2}}+12\,ab-20\,bc-30\,ac\]
C) \[9{{a}^{2}}+4{{b}^{2}}-5{{c}^{2}}-12\,ab-20\,bc+30\,ac\]
D) \[3{{a}^{2}}+4{{b}^{2}}-5{{c}^{2}}-12\,ab-20\,bc-30\,ac\]
Correct Answer: A
Solution :
(a): \[{{\left( 3a-2b+5c \right)}^{2}}-{{\left( 3a \right)}^{2}}+{{\left( -2b \right)}^{2}}+{{\left( 5c \right)}^{2}}\]\[+2\{3a\times \left( -2b \right)+\left( -2b \right)\times \left( 5c \right)+(3a\times 5c)\}\] \[=9{{a}^{2}}+4{{b}^{2}}+25{{c}^{2}}-12ab-20bc+30ac.\]
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