erweitern (x^2+2x+3)^7

Lösung

erweitern

(x^{2} + 2 x + 3)^{7}

x^{14} + 14 x^{13} + 105 x^{12} + 532 x^{11} + 2009 x^{10} + 5922 x^{9} + 13993 x^{8} + 26840 x^{7} + 41979 x^{6} + 53298 x^{5} + 54243 x^{4} + 43092 x^{3} + 25515 x^{2} + 10206 x + 2187

Schritte zur Lösung

(x^{2} + 2 x + 3)^{7}

(x^{2} + 2 x + 3)^{7} = (x^{2} + 2 x + 3) (x^{2} + 2 x + 3) (x^{2} + 2 x + 3) (x^{2} + 2 x + 3) (x^{2} + 2 x + 3) (x^{2} + 2 x + 3) (x^{2} + 2 x + 3)

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

Multipliziere aus

(x^{2} + 2 x + 3) (x^{2} + 2 x + 3) (x^{2} + 2 x + 3) (x^{2} + 2 x + 3) (x^{2} + 2 x + 3) (x^{2} + 2 x + 3) (x^{2} + 2 x + 3) : x^{14} + 14 x^{13} + 105 x^{12} + 532 x^{11} + 2009 x^{10} + 5922 x^{9} + 13993 x^{8} + 26840 x^{7} + 41979 x^{6} + 53298 x^{5} + 54243 x^{4} + 43092 x^{3} + 25515 x^{2} + 10206 x + 2187

= x^{14} + 14 x^{13} + 105 x^{12} + 532 x^{11} + 2009 x^{10} + 5922 x^{9} + 13993 x^{8} + 26840 x^{7} + 41979 x^{6} + 53298 x^{5} + 54243 x^{4} + 43092 x^{3} + 25515 x^{2} + 10206 x + 2187

e x p an d (a + b x + cy + d x^{2} + e y^{2} + f x y)^{2}

e x p an d 10 c + 10 - (\frac{100 ( 2 c - 8 )}{c ^{2} - 8 c + 20})

e x p an d e^{(y - \frac{( z - y ) ^{2}}{2 l ^{2} - t})}

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

e x p an d 2 (x - 1) + 3 (x - 2 - 5 (x + 3) = 8)