(x 3^{3} + x + x 5^{5} ) 17^{17}

asked by guest
on Mar 29, 2025 at 6:39 am



You asked:

Evaluate the expression: (x3+x+x5)17{\left( {x}^{3} + x + {x}^{5} \right)}^{17}

MathBot Answer:

Evaluated



(x3+x+x5)17=(x5+x3+x)17\displaystyle {\left( {x}^{3} + x + {x}^{5} \right)}^{17} = \left(x^{5} + x^{3} + x\right)^{17}

Expanded

(x3+x+x5)17=x85+17x83+153x81+952x79+4556x77+17748x75+58276x73+165104x71+410346x69+905658x67+1791426x65+3198312x63+5182008x61+7651632x59+10329336x57+12778152x55+14508939x53+15134931x51+14508939x49+12778152x47+10329336x45+7651632x43+5182008x41+3198312x39+1791426x37+905658x35+410346x33+165104x31+58276x29+17748x27+4556x25+952x23+153x21+17x19+x17{\left( {x}^{3} + x + {x}^{5} \right)}^{17} = x^{85} + 17 x^{83} + 153 x^{81} + 952 x^{79} + 4556 x^{77} + 17748 x^{75} + 58276 x^{73} + 165104 x^{71} + 410346 x^{69} + 905658 x^{67} + 1791426 x^{65} + 3198312 x^{63} + 5182008 x^{61} + 7651632 x^{59} + 10329336 x^{57} + 12778152 x^{55} + 14508939 x^{53} + 15134931 x^{51} + 14508939 x^{49} + 12778152 x^{47} + 10329336 x^{45} + 7651632 x^{43} + 5182008 x^{41} + 3198312 x^{39} + 1791426 x^{37} + 905658 x^{35} + 410346 x^{33} + 165104 x^{31} + 58276 x^{29} + 17748 x^{27} + 4556 x^{25} + 952 x^{23} + 153 x^{21} + 17 x^{19} + x^{17}

Factored

(x3+x+x5)17=x17(x2−x+1)17(x2+x+1)17{\left( {x}^{3} + x + {x}^{5} \right)}^{17} = x^{17} \left(x^{2} - x + 1\right)^{17} \left(x^{2} + x + 1\right)^{17}

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