erweitern (x-1/6)^2(x+5)(x+2/3)(x-8/6)

Lösung

erweitern

(x - \frac{1}{6})^{2} (x + 5) (x + \frac{2}{3}) (x - \frac{8}{6})

\frac{( 36 x ^{2} - 12 x + 1 ) x ^{3}}{36} + \frac{17 ( 36 x ^{2} - 12 x + 1 ) x ^{2}}{108} + \frac{5 ( 36 x ^{2} - 12 x + 1 ) x}{54} - \frac{( 36 x ^{2} - 12 x + 1 ) x ^{2}}{27} + \frac{- 612 x ^{3} - 156 x ^{2} + 103 x - 10}{81}

Schritte zur Lösung

(x - \frac{1}{6})^{2} (x + 5) (x + \frac{2}{3}) (x - \frac{8}{6})

Schreibe

(x - \frac{1}{6})^{2}

um:

\frac{36 x ^{2} - 12 x + 1}{36}

= \frac{36 x ^{2} - 12 x + 1}{36} (x + 5) (x + \frac{2}{3}) (x - \frac{8}{6})

Apply FOIL method

(x + 5) (x + \frac{2}{3}) : x^{2} + \frac{17 x}{3} + \frac{10}{3}

= \frac{36 x ^{2} - 12 x + 1}{36} (x^{2} + \frac{17 x}{3} + \frac{10}{3}) (x - \frac{8}{6})

Schreibe

\frac{36 x ^{2} - 12 x + 1}{36} (x - \frac{8}{6})

um:

\frac{( 36 x ^{2} - 12 x + 1 ) x}{36} - \frac{36 x ^{2} - 12 x + 1}{27}

= (\frac{( 36 x ^{2} - 12 x + 1 ) x}{36} - \frac{36 x ^{2} - 12 x + 1}{27}) (x^{2} + \frac{17 x}{3} + \frac{10}{3})

Setze Klammern

= \frac{( 36 x ^{2} - 12 x + 1 ) x}{36} x^{2} + \frac{( 36 x ^{2} - 12 x + 1 ) x}{36} \cdot \frac{17 x}{3} + \frac{( 36 x ^{2} - 12 x + 1 ) x}{36} \cdot \frac{10}{3} - \frac{36 x ^{2} - 12 x + 1}{27} x^{2} - \frac{36 x ^{2} - 12 x + 1}{27} \cdot \frac{17 x}{3} - \frac{36 x ^{2} - 12 x + 1}{27} \cdot \frac{10}{3}

Vereinfache

\frac{( 36 x ^{2} - 12 x + 1 ) x}{36} x^{2} + \frac{( 36 x ^{2} - 12 x + 1 ) x}{36} \cdot \frac{17 x}{3} + \frac{( 36 x ^{2} - 12 x + 1 ) x}{36} \cdot \frac{10}{3} - \frac{36 x ^{2} - 12 x + 1}{27} x^{2} - \frac{36 x ^{2} - 12 x + 1}{27} \cdot \frac{17 x}{3} - \frac{36 x ^{2} - 12 x + 1}{27} \cdot \frac{10}{3} : \frac{( 36 x ^{2} - 12 x + 1 ) x ^{3}}{36} + \frac{17 ( 36 x ^{2} - 12 x + 1 ) x ^{2}}{108} + \frac{5 ( 36 x ^{2} - 12 x + 1 ) x}{54} - \frac{( 36 x ^{2} - 12 x + 1 ) x ^{2}}{27} + \frac{- 612 x ^{3} - 156 x ^{2} + 103 x - 10}{81}

= \frac{( 36 x ^{2} - 12 x + 1 ) x ^{3}}{36} + \frac{17 ( 36 x ^{2} - 12 x + 1 ) x ^{2}}{108} + \frac{5 ( 36 x ^{2} - 12 x + 1 ) x}{54} - \frac{( 36 x ^{2} - 12 x + 1 ) x ^{2}}{27} + \frac{- 612 x ^{3} - 156 x ^{2} + 103 x - 10}{81}

f a c t or 44 n + 20 n^{2} - 15

s im pl i f y \frac{16}{2}

s im pl i f y (a - b)^{2} - (a + b)^{2}

\frac{7}{40}

e x p an d (y - 2) (y + 1)