faktorisieren a^{10}+b^{10}

Lösung

faktorisieren

a^{10} + b^{10}

(a^{2} + b^{2}) (a^{8} - a^{6} b^{2} + a^{4} b^{4} - a^{2} b^{6} + b^{8})

Schritte zur Lösung

a^{10} + b^{10}

Wende Exponentenregel an

= (a^{2})^{5} + (b^{2})^{5}

Apply factoring rule:

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1}), n i s o dd

(a^{2})^{5} + (b^{2})^{5} = (a^{2} + b^{2}) (a^{8} - a^{6} b^{2} + a^{4} b^{4} - a^{2} b^{6} + b^{8})

= (a^{2} + b^{2}) (a^{8} - a^{6} b^{2} + a^{4} b^{4} - a^{2} b^{6} + b^{8})

f a c t or 125 p^{3} + q^{3}

f a c t or 5 x^{3} \cdot y^{3} + 2 x \cdot y^{2}

s im pl i f y (sin (x)) \cdot [sin (x)]^{2} \cdot lo g_{1 + s i n (x)} (2)

s im pl i f y (x + 3) 2 + (y - 5) 2

e x p an d (2 x + 3 y)^{3} - 5 (2 x + 3 y)