erweitern (12x^6-3x+2)^5

Lösung

erweitern

(12 x^{6} - 3 x + 2)^{5}

248832 x^{30} - 311040 x^{25} + 207360 x^{24} + 155520 x^{20} - 207360 x^{19} + 69120 x^{18} - 38880 x^{15} + 77760 x^{14} - 51840 x^{13} + 11520 x^{12} + 4860 x^{10} - 12960 x^{9} + 12960 x^{8} - 5760 x^{7} + 960 x^{6} - 243 x^{5} + 810 x^{4} - 1080 x^{3} + 720 x^{2} - 240 x + 32

Schritte zur Lösung

(12 x^{6} - 3 x + 2)^{5}

(12 x^{6} - 3 x + 2)^{5} = (12 x^{6} - 3 x + 2) (12 x^{6} - 3 x + 2) (12 x^{6} - 3 x + 2) (12 x^{6} - 3 x + 2) (12 x^{6} - 3 x + 2)

= (12 x^{6} - 3 x + 2) (12 x^{6} - 3 x + 2) (12 x^{6} - 3 x + 2) (12 x^{6} - 3 x + 2) (12 x^{6} - 3 x + 2)

Multipliziere aus

(12 x^{6} - 3 x + 2) (12 x^{6} - 3 x + 2) (12 x^{6} - 3 x + 2) (12 x^{6} - 3 x + 2) (12 x^{6} - 3 x + 2) : 248832 x^{30} - 311040 x^{25} + 207360 x^{24} + 155520 x^{20} - 207360 x^{19} + 69120 x^{18} - 38880 x^{15} + 77760 x^{14} - 51840 x^{13} + 11520 x^{12} + 4860 x^{10} - 12960 x^{9} + 12960 x^{8} - 5760 x^{7} + 960 x^{6} - 243 x^{5} + 810 x^{4} - 1080 x^{3} + 720 x^{2} - 240 x + 32

= 248832 x^{30} - 311040 x^{25} + 207360 x^{24} + 155520 x^{20} - 207360 x^{19} + 69120 x^{18} - 38880 x^{15} + 77760 x^{14} - 51840 x^{13} + 11520 x^{12} + 4860 x^{10} - 12960 x^{9} + 12960 x^{8} - 5760 x^{7} + 960 x^{6} - 243 x^{5} + 810 x^{4} - 1080 x^{3} + 720 x^{2} - 240 x + 32

e x p an d A (x - 3) (x^{2} + 3)

e x p an d \frac{3 x + 5}{( x - 1 ) ( x + 1 )}

e x p an d - \frac{16 x}{( 4 + x ^{2} ) ^{2}}

e x p an d (9 - 2 x r i g h t) l e f t (9 - 2 x r i g h t) l e f t (x r i g h t)

e x p an d \frac{14 - 4 s}{( s - 3 ) ( s ^{2} + 3 s + 2 )}