simplify the expression

(t^2+1)(t^4+1)(t^4-t^2+1)(t^4+t^3+t^2-t+1)(t^4+t^3+t^2+t+1)

asked by guest
on Jan 18, 2025 at 2:17 am



You asked:

Simplify the expression: (t2+1)(t4+1)(t4−t2+1)(t4+t3+t2−t+1)(t4+t3+t2+t+1)\left({t}^{2} + 1\right) \left({t}^{4} + 1\right) \left({t}^{4} - {t}^{2} + 1\right) \left({t}^{4} + {t}^{3} + {t}^{2} - t + 1\right) \left({t}^{4} + {t}^{3} + {t}^{2} + t + 1\right)

MathBot Answer:

Expanded:

(t2+1)(t4+1)(t4−t2+1)(t4+t3+t2−t+1)(t4+t3+t2+t+1)=t18+2t17+3t16+2t15+4t14+4t13+5t12+4t11+7t10+4t9+5t8+4t7+5t6+2t5+4t4+2t3+t2+1 \left({t}^{2} + 1\right) \left({t}^{4} + 1\right) \left({t}^{4} - {t}^{2} + 1\right) \left({t}^{4} + {t}^{3} + {t}^{2} - t + 1\right) \left({t}^{4} + {t}^{3} + {t}^{2} + t + 1\right) = t^{18} + 2 t^{17} + 3 t^{16} + 2 t^{15} + 4 t^{14} + 4 t^{13} + 5 t^{12} + 4 t^{11} + 7 t^{10} + 4 t^{9} + 5 t^{8} + 4 t^{7} + 5 t^{6} + 2 t^{5} + 4 t^{4} + 2 t^{3} + t^{2} + 1

Factored:

(t2+1)(t4+1)(t4−t2+1)(t4+t3+t2−t+1)(t4+t3+t2+t+1)=(t2+1)(t4+1)(t4−t2+1)(t4+t3+t2−t+1)(t4+t3+t2+t+1) \left({t}^{2} + 1\right) \left({t}^{4} + 1\right) \left({t}^{4} - {t}^{2} + 1\right) \left({t}^{4} + {t}^{3} + {t}^{2} - t + 1\right) \left({t}^{4} + {t}^{3} + {t}^{2} + t + 1\right) = \left(t^{2} + 1\right) \left(t^{4} + 1\right) \left(t^{4} - t^{2} + 1\right) \left(t^{4} + t^{3} + t^{2} - t + 1\right) \left(t^{4} + t^{3} + t^{2} + t + 1\right)


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