If 2a+3b+c=0,then find the value of (2a)^3+(3b)^3+c^3
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If 2a+3b+c=0,then find the value of (2a)^3+(3b)^3+c^3![2a+3b+c=0\\\\ (a + b + c)^{3} = a^{3} + b^{3} + c^{3}+3a^{2}b+3a^{2}c + 3b^{2}c +3b^{2}a +3c^{2}a +3c^{2}a+6abc.\\\\=> (2a+3b+c)^{3}=0^{3}\\\\=>(2a)^{3}+(3b)^{3}+c^{3}+3(2a)^{2}(3b)+3(2a)^{2}c + 3(3b)^{2}c +3(3b)^{2}(2a) +3c^{2}(2a) +3c^{2}(2a)+6(2a)(3b)c=0\\\\=>(2a)^{3}+(3b)^{3}+c^{3}=-[(2a)^{2}(3b)+3(2a)^{2}c + 3(3b)^{2}c +3(3b)^{2}(2a) +3c^{2}(2a) +3c^{2}(2a)+6(2a)(3b)c]\\\\=>(2a)^{3}+(3b)^{3}+c^{3}=-(2a)^{2}(3b)-3(2a)^{2}c - 3(3b)^{2}c -3(3b)^{2}(2a) -3c^{2}(2a) -3c^{2}(2a)-6(2a)(3b)c](https://tex.z-dn.net/?f=2a%2B3b%2Bc%3D0%5C%5C%5C%5C+%28a+%2B+b+%2B+c%29%5E%7B3%7D+%3D+a%5E%7B3%7D+%2B+b%5E%7B3%7D+%2B+c%5E%7B3%7D%2B3a%5E%7B2%7Db%2B3a%5E%7B2%7Dc+%2B+3b%5E%7B2%7Dc+%2B3b%5E%7B2%7Da+%2B3c%5E%7B2%7Da+%2B3c%5E%7B2%7Da%2B6abc.%5C%5C%5C%5C%3D%26gt%3B+%282a%2B3b%2Bc%29%5E%7B3%7D%3D0%5E%7B3%7D%5C%5C%5C%5C%3D%26gt%3B%282a%29%5E%7B3%7D%2B%283b%29%5E%7B3%7D%2Bc%5E%7B3%7D%2B3%282a%29%5E%7B2%7D%283b%29%2B3%282a%29%5E%7B2%7Dc+%2B+3%283b%29%5E%7B2%7Dc+%2B3%283b%29%5E%7B2%7D%282a%29+%2B3c%5E%7B2%7D%282a%29+%2B3c%5E%7B2%7D%282a%29%2B6%282a%29%283b%29c%3D0%5C%5C%5C%5C%3D%26gt%3B%282a%29%5E%7B3%7D%2B%283b%29%5E%7B3%7D%2Bc%5E%7B3%7D%3D-%5B%282a%29%5E%7B2%7D%283b%29%2B3%282a%29%5E%7B2%7Dc+%2B+3%283b%29%5E%7B2%7Dc+%2B3%283b%29%5E%7B2%7D%282a%29+%2B3c%5E%7B2%7D%282a%29+%2B3c%5E%7B2%7D%282a%29%2B6%282a%29%283b%29c%5D%5C%5C%5C%5C%3D%26gt%3B%282a%29%5E%7B3%7D%2B%283b%29%5E%7B3%7D%2Bc%5E%7B3%7D%3D-%282a%29%5E%7B2%7D%283b%29-3%282a%29%5E%7B2%7Dc+-+3%283b%29%5E%7B2%7Dc+-3%283b%29%5E%7B2%7D%282a%29+-3c%5E%7B2%7D%282a%29+-3c%5E%7B2%7D%282a%29-6%282a%29%283b%29c "2a+3b+c=0\\\\ (a + b + c)^{3} = a^{3} + b^{3} + c^{3}+3a^{2}b+3a^{2}c + 3b^{2}c +3b^{2}a +3c^{2}a +3c^{2}a+6abc.\\\\=> (2a+3b+c)^{3}=0^{3}\\\\=>(2a)^{3}+(3b)^{3}+c^{3}+3(2a)^{2}(3b)+3(2a)^{2}c + 3(3b)^{2}c +3(3b)^{2}(2a) +3c^{2}(2a) +3c^{2}(2a)+6(2a)(3b)c=0\\\\=>(2a)^{3}+(3b)^{3}+c^{3}=-[(2a)^{2}(3b)+3(2a)^{2}c + 3(3b)^{2}c +3(3b)^{2}(2a) +3c^{2}(2a) +3c^{2}(2a)+6(2a)(3b)c]\\\\=>(2a)^{3}+(3b)^{3}+c^{3}=-(2a)^{2}(3b)-3(2a)^{2}c - 3(3b)^{2}c -3(3b)^{2}(2a) -3c^{2}(2a) -3c^{2}(2a)-6(2a)(3b)c")
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