erweitern (xsin(θ)+ycos(θ))^2

Lösung

erweitern

(x sin (θ) + y cos (θ))^{2}

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

Schritte zur Lösung

(x sin (θ) + y cos (θ))^{2}

Wende Formel für perfekte quadratische Gleichungen an:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

Vereinfache

(x sin (θ))^{2} + 2 x sin (θ) y cos (θ) + (y cos (θ))^{2} : y^{2} cos^{2} (θ) + x^{2} sin^{2} (θ) + x y sin (2 θ)

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

e x p an d \frac{4 x ( x ^{3} + 2 ) + 3 x ^{2}}{2 ( x ^{3} + 2 ) ^{\frac{1}{2}}}

e x p an d (17 - 3) (6 + 2)

e x p an d \frac{s ^{2} + 12}{( s ^{2} + 9 ) ( x + 2 ) ( x + 1 ) ( x - 1 )}

e x p an d 6 (4 a)

e x p an d \frac{12 x - 4 x ^{2}}{( x + 3 ) ^{2}}