erweitern np*(np-p+1)^2

Lösung

erweitern

n p \cdot (n p - p + 1)^{2}

n^{3} p^{3} - 2 n^{2} p^{3} + 2 n^{2} p^{2} + n p^{3} - 2 n p^{2} + n p

Schritte zur Lösung

n p (n p - p + 1)^{2}

(n p - p + 1)^{2} = n^{2} p^{2} - 2 n p^{2} + 2 n p + p^{2} - 2 p + 1

= n p (n^{2} p^{2} + p^{2} - 2 n p^{2} + 2 n p - 2 p + 1)

Setze Klammern

= n p n^{2} p^{2} + n p (- 2 n p^{2}) + n p \cdot 2 n p + n p p^{2} + n p (- 2 p) + n p \cdot 1

Wende Minus-Plus Regeln an

+ (- a) = - a

= n^{2} n p^{2} p - 2 nn p^{2} p + 2 nn pp + n p^{2} p - 2 n pp + 1 \cdot n p

Vereinfache

n^{2} n p^{2} p - 2 nn p^{2} p + 2 nn pp + n p^{2} p - 2 n pp + 1 \cdot n p : n^{3} p^{3} - 2 n^{2} p^{3} + 2 n^{2} p^{2} + n p^{3} - 2 n p^{2} + n p

= n^{3} p^{3} - 2 n^{2} p^{3} + 2 n^{2} p^{2} + n p^{3} - 2 n p^{2} + n p

e x p an d \frac{- x + a}{( a + ab ) ( - ba + a )}

e x p an d 3 (x)^{2}

e x p an d (6 x + 3 y = 1, 8) (x + y = 4)

e x p an d (3 x^{2} - 14 x + 16) \circ (x - 5)

e x p an d \frac{3}{( 5 - 4 x ) ^{4}}