erweitern sqrt(144t^2+(9cos^2(t)+9cos(t)sin(t))^2)

Lösung

erweitern

144 t^{2} + (9 cos^{2} (t) + 9 cos (t) sin (t))^{2}

3 16 t^{2} + 9 cos^{4} (t) + 18 cos^{3} (t) sin (t) + 9 cos^{2} (t) sin^{2} (t)

Schritte zur Lösung

144 t^{2} + (9 cos^{2} (t) + 9 cos (t) sin (t))^{2}

Multipliziere aus

144 t^{2} + (9 cos^{2} (t) + 9 cos (t) sin (t))^{2} : 144 t^{2} + 81 cos^{4} (t) + 162 cos^{3} (t) sin (t) + 81 cos^{2} (t) sin^{2} (t)

= 144 t^{2} + 81 cos^{4} (t) + 162 cos^{3} (t) sin (t) + 81 cos^{2} (t) sin^{2} (t)

Faktorisiere

144 t^{2} + 81 cos^{4} (t) + 162 cos^{3} (t) sin (t) + 81 cos^{2} (t) sin^{2} (t) : 9 (16 t^{2} + 9 cos^{4} (t) + 18 cos^{3} (t) sin (t) + 9 cos^{2} (t) sin^{2} (t))

= 9 (16 t^{2} + 9 cos^{4} (t) + 18 cos^{3} (t) sin (t) + 9 cos^{2} (t) sin^{2} (t))

Wende Radikal Regel an:

n ab = n a n b,

angenommen

a \geq 0, b \geq 0

= 9 16 t^{2} + 9 cos^{4} (t) + 18 cos^{3} (t) sin (t) + 9 cos^{2} (t) sin^{2} (t)

9 = 3

= 3 16 t^{2} + 9 cos^{4} (t) + 18 cos^{3} (t) sin (t) + 9 cos^{2} (t) sin^{2} (t)

e x p an d (2 r cos (t) + x cos (t))^{2}

e x p an d (x + 7) 7 x - 9

e x p an d (6 + 5) {+}

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

e x p an d c (l - a - b - y)^{2}