faktorisieren-(x+2y)^2+16(x+y)^2

Lösung

faktorisieren

- (x + 2 y)^{2} + 16 (x + y)^{2}

(5 x + 6 y) (3 x + 2 y)

Schritte zur Lösung

- (x + 2 y)^{2} + 16 (x + y)^{2}

Schreibe

16 (x + y)^{2} - (x + 2 y)^{2}

um:

(4 (x + y))^{2} - (x + 2 y)^{2}

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

Wende Formel zur Differenz von zwei Quadraten an:

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

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

= (4 (x + y) + (x + 2 y)) (4 (x + y) - (x + 2 y))

Fasse zusammen

= (x + 2 y + 4 (x + y)) (4 (x + y) - x - 2 y)

Multipliziere aus

4 (x + y) + x + 2 y : 5 x + 6 y

= (5 x + 6 y) (4 (x + y) - x - 2 y)

Multipliziere aus

4 (x + y) - x - 2 y : 3 x + 2 y

= (5 x + 6 y) (3 x + 2 y)

s im pl i f y \frac{n ^{2}}{n ^{4}}

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

2 (1.5 x - 2.1) + 1.7 \geq 2 (2.4 x - 3.5)

3 x^{2} - 4 x + 6 = 2

- \frac{2}{3} (0) - 1