erweitern (2x+2y)(x+y)cos(x^2+2xy+y^2)

Lösung

erweitern

(2 x + 2 y) (x + y) cos (x^{2} + 2 x y + y^{2})

2 x^{2} cos (x^{2} + 2 x y + y^{2}) + 4 x y cos (x^{2} + 2 x y + y^{2}) + 2 y^{2} cos (x^{2} + 2 x y + y^{2})

Schritte zur Lösung

(2 x + 2 y) (x + y) cos (x^{2} + 2 x y + y^{2})

= cos (x^{2} + 2 x y + y^{2}) (2 x + 2 y) (x + y)

Apply FOIL method

(2 x + 2 y) (x + y) : 2 x^{2} + 4 x y + 2 y^{2}

= cos (x^{2} + 2 x y + y^{2}) (2 x^{2} + 4 x y + 2 y^{2})

Wende das Distributivgesetz an:

m (a + b + c) = ma + mb + m c

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

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

= 2 x^{2} cos (x^{2} + 2 x y + y^{2}) + 4 x y cos (x^{2} + 2 x y + y^{2}) + 2 y^{2} cos (x^{2} + 2 x y + y^{2})

e x p an d \frac{t ( x ^{2} + 2 x )}{( x + 1 )}

e x p an d (7 - 2) (5 + 3)

e x p an d (- y e^{5} + 3 y e^{3} - y e^{7} + 4 y + 10) \cdot (5 y e^{2})

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

e x p an d (2 - 2)^{4}