erweitern ((bg-log_{10}(a+b))^2)/(l^4a^6)

Lösung

erweitern

\frac{( b g - lo g _{10} ( a + b ) ) ^{2}}{l ^{4} a ^{6}}

\frac{b ^{2} g ^{2}}{l ^{4} a ^{6}} - \frac{2 b g lo g _{10} ( a + b )}{l ^{4} a ^{6}} + \frac{lo g _{10} ( a + b ) ^{2}}{l ^{4} a ^{6}}

Schritte zur Lösung

\frac{( b g - lo g _{10} ( a + b ) ) ^{2}}{l ^{4} a ^{6}}

(b g - lo g_{10} (a + b))^{2} = b^{2} g^{2} - 2 b g lo g_{10} (a + b) + lo g_{10} (a + b)^{2}

= \frac{b ^{2} g ^{2} - 2 b g lo g _{10} ( b + a ) + lo g _{10} ( b + a ) ^{2}}{l ^{4} a ^{6}}

Wende Bruchregel an:

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

\frac{b ^{2} g ^{2} - 2 b g lo g _{10} ( a + b ) + lo g _{10} ( a + b ) ^{2}}{l ^{4} a ^{6}} = \frac{b ^{2} g ^{2}}{l ^{4} a ^{6}} - \frac{2 b g lo g _{10} ( a + b )}{l ^{4} a ^{6}} + \frac{lo g _{10} ( a + b ) ^{2}}{l ^{4} a ^{6}}

= \frac{b ^{2} g ^{2}}{l ^{4} a ^{6}} - \frac{2 b g lo g _{10} ( b + a )}{l ^{4} a ^{6}} + \frac{lo g _{10} ( b + a ) ^{2}}{l ^{4} a ^{6}}

s im pl i f y (z + \frac{3}{2}) (z - \frac{3}{2})

e x p an d (1 - cos (8 x))^{3}

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

s im pl i f y 5 (5 + 7)

s im pl i f y 4 (5 - 1)