erweitern (0.9a+1.1b+1.1c+(4d)/3)^2

Lösung

erweitern

(0.9 a + 1.1 b + 1.1 c + \frac{4 d}{3})^{2}

\frac{81 a ^{2} + 121 b ^{2} + 121 c ^{2}}{100} + \frac{99 ab + 99 a c + 121 b c}{50} + \frac{12 a d}{5} + \frac{44 b d + 44 c d}{15} + \frac{16 d ^{2}}{9}

Schritte zur Lösung

(0.9 a + 1.1 b + 1.1 c + \frac{4 d}{3})^{2}

Wende Exponentenregel an:

a^{b + c} = a^{b} \cdot a^{c}

(0.9 a + 1.1 b + 1.1 c + \frac{4 d}{3})^{2} = (0.9 a + 1.1 b + 1.1 c + \frac{4 d}{3}) (0.9 a + 1.1 b + 1.1 c + \frac{4 d}{3})

= (0.9 a + 1.1 b + 1.1 c + \frac{4 d}{3}) (0.9 a + 1.1 b + 1.1 c + \frac{4 d}{3})

Setze Klammern

= 0.9 a \cdot 0.9 a + 0.9 a \cdot 1.1 b + 0.9 a \cdot 1.1 c + 0.9 a \frac{4 d}{3} + 1.1 b \cdot 0.9 a + 1.1 b \cdot 1.1 b + 1.1 b \cdot 1.1 c + 1.1 b \frac{4 d}{3} + 1.1 c \cdot 0.9 a + 1.1 c \cdot 1.1 b + 1.1 c \cdot 1.1 c + 1.1 c \frac{4 d}{3} + \frac{4 d}{3} \cdot 0.9 a + \frac{4 d}{3} \cdot 1.1 b + \frac{4 d}{3} \cdot 1.1 c + \frac{4 d}{3} \cdot \frac{4 d}{3}

Vereinfache

0.9 a \cdot 0.9 a + 0.9 a \cdot 1.1 b + 0.9 a \cdot 1.1 c + 0.9 a \frac{4 d}{3} + 1.1 b \cdot 0.9 a + 1.1 b \cdot 1.1 b + 1.1 b \cdot 1.1 c + 1.1 b \frac{4 d}{3} + 1.1 c \cdot 0.9 a + 1.1 c \cdot 1.1 b + 1.1 c \cdot 1.1 c + 1.1 c \frac{4 d}{3} + \frac{4 d}{3} \cdot 0.9 a + \frac{4 d}{3} \cdot 1.1 b + \frac{4 d}{3} \cdot 1.1 c + \frac{4 d}{3} \cdot \frac{4 d}{3} : \frac{81 a ^{2} + 121 b ^{2} + 121 c ^{2}}{100} + \frac{99 ab + 99 a c + 121 b c}{50} + \frac{12 a d}{5} + \frac{44 b d + 44 c d}{15} + \frac{16 d ^{2}}{9}

= \frac{81 a ^{2} + 121 b ^{2} + 121 c ^{2}}{100} + \frac{99 ab + 99 a c + 121 b c}{50} + \frac{12 a d}{5} + \frac{44 b d + 44 c d}{15} + \frac{16 d ^{2}}{9}

e x p an d s (s = 180 n - 360)

e x p an d (3 t (x) - 5) x t^{'}

e x p an d \frac{( 2 - x ) ( x - 3 ) ( x - 4 )}{24}

s im pl i f y (5 + sin (t))^{2} + cos^{2} (t)

e x p an d \frac{378.7 ( s + 1 )}{s ^{4} + 30 s ^{3} + 100 s ^{2} - 200 s + 400}