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Beliebt Rechnen >

erweitern (x^2+x^3)^4

Lösung

erweitern

(x^{2} + x^{3})^{4}

Lösung

x^{8} + 4 x^{9} + 6 x^{10} + 4 x^{11} + x^{12}

Schritte zur Lösung

(x^{2} + x^{3})^{4}

Wende Binomialsetz an:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x^{2}, b = x^{3}

= i = 0 \sum 4 (i 4) (x^{2})^{(4 - i)} (x^{3})^{i}

Erweitere Summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (x^{2})^{4} (x^{3})^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} (x^{3})^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (x^{2})^{2} (x^{3})^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (x^{2})^{1} (x^{3})^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} (x^{3})^{4}

Vereinfache

\frac{4 !}{0 ! ( 4 - 0 ) !} (x^{2})^{4} (x^{3})^{0} : x^{8}

Vereinfache

\frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} (x^{3})^{1} : 4 x^{9}

Vereinfache

\frac{4 !}{2 ! ( 4 - 2 ) !} (x^{2})^{2} (x^{3})^{2} : 6 x^{10}

Vereinfache

\frac{4 !}{3 ! ( 4 - 3 ) !} (x^{2})^{1} (x^{3})^{3} : 4 x^{11}

Vereinfache

\frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} (x^{3})^{4} : x^{12}

= x^{8} + 4 x^{9} + 6 x^{10} + 4 x^{11} + x^{12}

Beliebte Beispiele

integral of t/((t^2+1)^{7/2)}

\int \frac{t}{( t ^{2} + 1 ) ^{\frac{7}{2}}} d t

fläche y=2x^2-1,(0,3)

a re a y = 2 x^{2} - 1, (0, 3)

y^{''}+4y^'+4y=4e^{-2t}

y^{^{''}} + 4 y^{^{'}} + 4 y = 4 e^{- 2 t}

integral of ((x-3))/((x+4)(x-5))

\int \frac{( x - 3 )}{( x + 4 ) ( x - 5 )} d x

derivative of x^3-5x^2+7x-3

\frac{d}{d x} (x^{3} - 5 x^{2} + 7 x - 3)