erweitern 4((y-a-bx)/c)^2

Lösung

erweitern

4 (\frac{y - a - b x}{c})^{2}

- \frac{8 a y}{c ^{2}} - \frac{8 b y x}{c ^{2}} + \frac{4 y ^{2}}{c ^{2}} + \frac{4 a ^{2}}{c ^{2}} + \frac{8 ab x}{c ^{2}} + \frac{4 b ^{2} x ^{2}}{c ^{2}}

Schritte zur Lösung

4 (\frac{y - a - b x}{c})^{2}

(\frac{y - a - b x}{c})^{2} = \frac{- 2 a y - 2 b y x + y ^{2} + a ^{2} + 2 ab x + b ^{2} x ^{2}}{c ^{2}}

= 4 \cdot \frac{y ^{2} - 2 a y - 2 b y x + a ^{2} + 2 ab x + b ^{2} x ^{2}}{c ^{2}}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( - 2 a y - 2 b y x + y ^{2} + a ^{2} + 2 ab x + b ^{2} x ^{2} ) \cdot 4}{c ^{2}}

Multipliziere aus

(- 2 a y - 2 b y x + y^{2} + a^{2} + 2 ab x + b^{2} x^{2}) \cdot 4 : - 8 a y - 8 b y x + 4 y^{2} + 4 a^{2} + 8 ab x + 4 b^{2} x^{2}

= \frac{- 8 a y - 8 b y x + 4 y ^{2} + 4 a ^{2} + 8 ab x + 4 b ^{2} x ^{2}}{c ^{2}}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- 8 a y - 8 b y x + 4 y ^{2} + 4 a ^{2} + 8 ab x + 4 b ^{2} x ^{2}}{c ^{2}} = - \frac{8 a y}{c ^{2}} - \frac{8 b y x}{c ^{2}} + \frac{4 y ^{2}}{c ^{2}} + \frac{4 a ^{2}}{c ^{2}} + \frac{8 ab x}{c ^{2}} + \frac{4 b ^{2} x ^{2}}{c ^{2}}

= - \frac{8 a y}{c ^{2}} - \frac{8 b y x}{c ^{2}} + \frac{4 y ^{2}}{c ^{2}} + \frac{4 a ^{2}}{c ^{2}} + \frac{8 ab x}{c ^{2}} + \frac{4 b ^{2} x ^{2}}{c ^{2}}

e x p an d \frac{( x - y ) x}{b ( x + y )}

e x p an d 2 \cdot (x - y) - 4 c d o t (y - x)

e x p an d (e^{t} - 1)^{3} e^{5 t}

e x p an d \frac{784000 ( - 2394 ln ( 21 ) + 33080 )}{ln ( 21 )}

e x p an d \frac{4 + 2 s}{s \cdot ( s - 4 ) ( s - 1 )}