erweitern (a+b-(at)/(10))^2*t

Lösung

erweitern

(a + b - \frac{a t}{10})^{2} \cdot t

2 ab t + a^{2} t - \frac{a ^{2} t ^{2}}{5} - \frac{ab t ^{2}}{5} + \frac{a ^{2} t ^{3}}{100} + b^{2} t

Schritte zur Lösung

(a + b - \frac{a t}{10})^{2} t

(a + b - \frac{a t}{10})^{2} = 2 ab + a^{2} + \frac{- a ^{2} t - ab t}{5} + \frac{a ^{2} t ^{2}}{100} + b^{2}

= t (a^{2} + 2 ab + \frac{a ^{2} t ^{2}}{100} + \frac{- a ^{2} t - ab t}{5} + b^{2})

= t (2 ab + a^{2} + \frac{- a ^{2} t - ab t}{5} + \frac{a ^{2} t ^{2}}{100} + b^{2})

Setze Klammern

= t \cdot 2 ab + t a^{2} + t \frac{- a ^{2} t - ab t}{5} + t \frac{a ^{2} t ^{2}}{100} + t b^{2}

= 2 ab t + a^{2} t + \frac{- a ^{2} t - ab t}{5} t + \frac{a ^{2} t ^{2}}{100} t + b^{2} t

Vereinfache

2 ab t + a^{2} t + \frac{- a ^{2} t - ab t}{5} t + \frac{a ^{2} t ^{2}}{100} t + b^{2} t : 2 ab t + a^{2} t + \frac{- a ^{2} t ^{2} - ab t ^{2}}{5} + \frac{a ^{2} t ^{3}}{100} + b^{2} t

= 2 ab t + a^{2} t + \frac{- a ^{2} t ^{2} - ab t ^{2}}{5} + \frac{a ^{2} t ^{3}}{100} + b^{2} t

Wende Bruchregel an:

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

\frac{- a ^{2} t ^{2} - ab t ^{2}}{5} = - \frac{a ^{2} t ^{2}}{5} - \frac{ab t ^{2}}{5}

= 2 ab t + a^{2} t - \frac{a ^{2} t ^{2}}{5} - \frac{ab t ^{2}}{5} + \frac{a ^{2} t ^{3}}{100} + b^{2} t

e x p an d p (5, 6) y q (2, - 3)

e x p an d - 1.5 (l + s = 9)

e x p an d \frac{x ^{2} + 8 x + 15}{( x + 4 ) ^{2}}

e x p an d \frac{1}{( ( x - b ) ( x - c ) )}

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