espandere ((11x^4+2)^5)/2

Soluzione

espandere

\frac{( 11 x ^{4} + 2 ) ^{5}}{2}

\frac{161051 x ^{20}}{2} + 73205 x^{16} + 26620 x^{12} + 4840 x^{8} + 440 x^{4} + 16

Fasi della soluzione

\frac{( 11 x ^{4} + 2 ) ^{5}}{2}

(11 x^{4} + 2)^{5} = 161051 x^{20} + 146410 x^{16} + 53240 x^{12} + 9680 x^{8} + 880 x^{4} + 32

= \frac{161051 x ^{20} + 146410 x ^{16} + 53240 x ^{12} + 9680 x ^{8} + 880 x ^{4} + 32}{2}

Applica la regola delle frazioni:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{161051 x ^{20} + 146410 x ^{16} + 53240 x ^{12} + 9680 x ^{8} + 880 x ^{4} + 32}{2} = \frac{161051 x ^{20}}{2} + \frac{146410 x ^{16}}{2} + \frac{53240 x ^{12}}{2} + \frac{9680 x ^{8}}{2} + \frac{880 x ^{4}}{2} + \frac{32}{2}

= \frac{161051 x ^{20}}{2} + \frac{146410 x ^{16}}{2} + \frac{53240 x ^{12}}{2} + \frac{9680 x ^{8}}{2} + \frac{880 x ^{4}}{2} + \frac{32}{2}

\frac{146410 x ^{16}}{2} = 73205 x^{16}

\frac{53240 x ^{12}}{2} = 26620 x^{12}

\frac{9680 x ^{8}}{2} = 4840 x^{8}

\frac{880 x ^{4}}{2} = 440 x^{4}

\frac{32}{2} = 16

= \frac{161051 x ^{20}}{2} + 73205 x^{16} + 26620 x^{12} + 4840 x^{8} + 440 x^{4} + 16

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e x p an d ln (x) (x ln (x) - x)