erweitern xsqrt(2x-1)(x^2+3)^2

Lösung

erweitern

x 2 x - 1 (x^{2} + 3)^{2}

x^{5} 2 x - 1 + 6 x^{3} 2 x - 1 + 9 x 2 x - 1

Schritte zur Lösung

x 2 x - 1 (x^{2} + 3)^{2}

= x (x^{2} + 3)^{2} 2 x - 1

Schreibe

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

um:

x^{4} + 6 x^{2} + 9

= x (x^{4} + 6 x^{2} + 9) 2 x - 1

= x 2 x - 1 (x^{4} + 6 x^{2} + 9)

Wende das Distributivgesetz an:

m (a + b + c) = ma + mb + m c

x 2 x - 1 (x^{4} + 6 x^{2} + 9) = x 2 x - 1 x^{4} + x 2 x - 1 \cdot 6 x^{2} + x 2 x - 1 \cdot 9

= x 2 x - 1 x^{4} + x 2 x - 1 \cdot 6 x^{2} + x 2 x - 1 \cdot 9

Vereinfache

x 2 x - 1 x^{4} + x 2 x - 1 \cdot 6 x^{2} + x 2 x - 1 \cdot 9 : x^{5} 2 x - 1 + 6 x^{3} 2 x - 1 + 9 x 2 x - 1

= x^{5} 2 x - 1 + 6 x^{3} 2 x - 1 + 9 x 2 x - 1

e x p an d \frac{2500 ( - 104 + 43 3 )}{5787}

e x p an d \frac{12 x}{( 1 - x ^{2} ) ^{2}}

e x p an d \frac{5 x ^{2} + 6 x + 9}{( x - 3 ) ^{2} \cdot ( x + 1 ) ^{2}}

e x p an d \frac{2 n}{( 1 - x ) ^{2}}

e x p an d (tan (z) - sin (x) sin (y)) d x + cos (x) cos (y) d y