vereinfachen (x^2+4)^2(x+2i)^2

Lösung

vereinfachen

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

(x^{6} + 4 x^{4} - 16 x^{2} - 64) + (4 x^{5} + 32 x^{3} + 64 x) i

Schritte zur Lösung

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

Schreibe

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

um:

x^{4} + 8 x^{2} + 16

= (x^{4} + 8 x^{2} + 16) (x + 2 i)^{2}

= (x + 2 i)^{2} (x^{4} + 8 x^{2} + 16)

Schreibe

(x + 2 i)^{2}

um:

x^{2} + 4 x i - 4

= (x^{2} + 4 x i - 4) (x^{4} + 8 x^{2} + 16)

Setze Klammern

= x^{2} x^{4} + x^{2} \cdot 8 x^{2} + x^{2} \cdot 16 + 4 x i x^{4} + 4 x i 8 x^{2} + 4 x i 16 - 4 x^{4} - 4 \cdot 8 x^{2} - 4 \cdot 16

Vereinfache

x^{2} x^{4} + x^{2} \cdot 8 x^{2} + x^{2} \cdot 16 + 4 x i x^{4} + 4 x i 8 x^{2} + 4 x i 16 - 4 x^{4} - 4 \cdot 8 x^{2} - 4 \cdot 16 : x^{6} + 4 x^{4} - 16 x^{2} + 4 x^{5} i + 32 x^{3} i + 64 x i - 64

= x^{6} + 4 x^{4} - 16 x^{2} + 4 x^{5} i + 32 x^{3} i + 64 x i - 64

Rewrite in standard complex form:

(x^{6} + 4 x^{4} - 16 x^{2} - 64) + (4 x^{5} + 32 x^{3} + 64 x) i

= (x^{6} + 4 x^{4} - 16 x^{2} - 64) + (4 x^{5} + 32 x^{3} + 64 x) i

s im pl i f y (- 4 x + 5) (\frac{3}{2})

e x p an d \frac{- x ^{2} + 2 x + 4}{( x ^{2} + 4 ) ^{2}}

e x p an d R A TE (5, 94.25, - 270.34 - 40)

e x p an d \frac{( a + 2 ) + ( a + 3 ) !}{( a + 2 ) ! ( a + 4 )}

e x p an d (2 + 37)^{4}