vereinfachen (a+b+c)[(a-b)^2+(b-c)^2+(c-a)^2]

Lösung

vereinfachen

(a + b + c) [(a - b)^{2} + (b - c)^{2} + (c - a)^{2}]

(a + b + c) (2 a^{2} - 2 ab + 2 b^{2} - 2 b c + 2 c^{2} - 2 a c)

Schritte zur Lösung

(a + b + c) ((a - b)^{2} + (b - c)^{2} + (c - a)^{2})

Schreibe

(a - b)^{2}

um:

a^{2} - 2 ab + b^{2}

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

Schreibe

(b - c)^{2}

um:

b^{2} - 2 b c + c^{2}

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

Schreibe

(c - a)^{2}

um:

c^{2} - 2 a c + a^{2}

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

Vereinfache

a^{2} - 2 ab + b^{2} + b^{2} - 2 b c + c^{2} + c^{2} - 2 a c + a^{2} : 2 a^{2} - 2 ab + 2 b^{2} - 2 b c + 2 c^{2} - 2 a c

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

s im pl i f y 8 (x + y)^{3} - 27 (x - y)^{3}

s im pl i f y (3 x^{3})^{2} \cdot 4 x^{3}

s im pl i f y (\frac{3 p + q}{3})^{2}

s im pl i f y 24 \frac{n ^{2}}{n} + 32 \frac{n}{n} + \frac{12}{n}

s im pl i f y (x^{3} y^{3} - 6) (x^{3} y^{3} - 6)