erweitern 4(1/2 x+1/2 y)^2+2(x+y)^2

Lösung

erweitern

4 (\frac{1}{2} x + \frac{1}{2} y)^{2} + 2 (x + y)^{2}

3 x^{2} + 3 y^{2} + 6 x y

Schritte zur Lösung

4 (\frac{1}{2} x + \frac{1}{2} y)^{2} + 2 (x + y)^{2}

Schreibe

4 (\frac{1}{2} x + \frac{1}{2} y)^{2}

um:

4 \cdot \frac{x ^{2} + y ^{2} + 2 x y}{4}

= 4 \cdot \frac{x ^{2} + y ^{2} + 2 x y}{4} + 2 (x + y)^{2}

Schreibe

2 (x + y)^{2}

um:

2 x^{2} + 4 x y + 2 y^{2}

= 4 \cdot \frac{x ^{2} + y ^{2} + 2 x y}{4} + 2 x^{2} + 4 x y + 2 y^{2}

Vereinfache

4 \cdot \frac{x ^{2} + y ^{2} + 2 x y}{4} + 2 x^{2} + 4 x y + 2 y^{2} : 3 x^{2} + 3 y^{2} + 6 x y

= 3 x^{2} + 3 y^{2} + 6 x y

e x p an d 3 x (6 - x^{2}) d x

s im pl i f y (- r (3 + 11) + 33)^{2}

e x p an d f (tan (x) + h) - tan (x)

e x p an d p^{\frac{3}{4}} (p^{\frac{1}{4}} + 3 p^{\frac{5}{4}})

e x p an d [x - \frac{x ^{3}}{3 !} + \frac{x ^{5}}{5 !}]^{2}