erweitern (3x-y)(3x+y)(9x^2+y^2)^2

Lösung

erweitern

(3 x - y) (3 x + y) (9 x^{2} + y^{2})^{2}

729 x^{6} + 81 x^{4} y^{2} - 18 x^{2} y^{4} + 9 y^{4} x^{2} - y^{6}

Schritte zur Lösung

(3 x - y) (3 x + y) (9 x^{2} + y^{2})^{2}

= (9 x^{2} + y^{2})^{2} (3 x - y) (3 x + y)

Apply Difference of Two Squares

(3 x - y) (3 x + y) : 9 x^{2} - y^{2}

= (9 x^{2} + y^{2})^{2} (9 x^{2} - y^{2})

Schreibe

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

um:

81 x^{4} + 18 x^{2} y^{2} + y^{4}

= (81 x^{4} + 18 x^{2} y^{2} + y^{4}) (9 x^{2} - y^{2})

Setze Klammern

= 81 x^{4} \cdot 9 x^{2} + 81 x^{4} (- y^{2}) + 18 x^{2} y^{2} \cdot 9 x^{2} + 18 x^{2} y^{2} (- y^{2}) + y^{4} \cdot 9 x^{2} + y^{4} (- y^{2})

Vereinfache

81 x^{4} \cdot 9 x^{2} + 81 x^{4} (- y^{2}) + 18 x^{2} y^{2} \cdot 9 x^{2} + 18 x^{2} y^{2} (- y^{2}) + y^{4} \cdot 9 x^{2} + y^{4} (- y^{2}) : 729 x^{6} + 81 x^{4} y^{2} - 18 x^{2} y^{4} + 9 y^{4} x^{2} - y^{6}

= 729 x^{6} + 81 x^{4} y^{2} - 18 x^{2} y^{4} + 9 y^{4} x^{2} - y^{6}

e x p an d (x^{2} - 1) (2 x - 1)

s im pl i f y 2 6^{6}

e x p an d (x^{2} - 6 x + 10)^{2}

f a c t or 25 a^{2} - 49 b^{2}

s im pl i f y 5^{1 + l o g_{5} (3)}