erweitern (rcos(θ)+rsin(θ)+x)^2r

Lösung

erweitern

(r cos (θ) + r sin (θ) + x)^{2} r

r^{3} cos^{2} (θ) + r^{3} sin (2 θ) + 2 r^{2} x cos (θ) + r^{3} sin^{2} (θ) + 2 r^{2} x sin (θ) + r x^{2}

Schritte zur Lösung

(r cos (θ) + r sin (θ) + x)^{2} r

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

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

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

Setze Klammern

= r r^{2} cos^{2} (θ) + r sin (2 θ) r^{2} + r \cdot 2 r x cos (θ) + r r^{2} sin^{2} (θ) + r \cdot 2 r x sin (θ) + r x^{2}

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

Vereinfache

r^{2} r cos^{2} (θ) + r^{2} r sin (2 θ) + 2 rr x cos (θ) + r^{2} r sin^{2} (θ) + 2 rr x sin (θ) + r x^{2} : r^{3} cos^{2} (θ) + r^{3} sin (2 θ) + 2 r^{2} x cos (θ) + r^{3} sin^{2} (θ) + 2 r^{2} x sin (θ) + r x^{2}

= r^{3} cos^{2} (θ) + r^{3} sin (2 θ) + 2 r^{2} x cos (θ) + r^{3} sin^{2} (θ) + 2 r^{2} x sin (θ) + r x^{2}

e x p an d (7, 67 + 5, 87 - 5, 780, 5) x (3, 56 + 1, 2)

e x p an d 3 ((5, - 3, 2) - 2 (1, 7, - 2))

e x p an d x (x - ln (x))

e x p an d (f \circ 2 x^{2} + 1) (x + 1)

e x p an d e^{4 x} \cdot (38 - 7 x)