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Beliebt Algebra >

faktorisieren 81(7a+3)^4-72(7a+3)^2+16

Lösung

faktorisieren

81 (7 a + 3)^{4} - 72 (7 a + 3)^{2} + 16

Lösung

49 (21 a + 11)^{2} (3 a + 1)^{2}

Schritte zur Lösung

81 (7 a + 3)^{4} - 72 (7 a + 3)^{2} + 16

Angenommen

u = (7 a + 3)^{2}

= 81 u^{2} - 72 u + 16

Faktorisiere

81 u^{2} - 72 u + 16 : (9 u - 4) (9 u - 4)

= (9 u - 4) (9 u - 4)

Setze in

u = (7 a + 3)^{2}

ein

= (9 (7 a + 3)^{2} - 4) (9 (7 a + 3)^{2} - 4)

Faktorisiere

9 (7 a + 3)^{2} - 4 : (3 (7 a + 3) + 2) (3 (7 a + 3) - 2)

= (3 (7 a + 3) + 2) (3 (7 a + 3) - 2) (9 (7 a + 3)^{2} - 4)

Faktorisiere

9 (7 a + 3)^{2} - 4 : (3 (7 a + 3) + 2) (3 (7 a + 3) - 2)

= (3 (7 a + 3) + 2) (3 (7 a + 3) - 2) (3 (7 a + 3) + 2) (3 (7 a + 3) - 2)

Fasse zusammen

= (3 (7 a + 3) + 2)^{2} (3 (7 a + 3) - 2)^{2}

(3 (7 a + 3) + 2)^{2} = (21 a + 11)^{2}

= (21 a + 11)^{2} (3 (7 a + 3) - 2)^{2}

(3 (7 a + 3) - 2)^{2} = 49 (3 a + 1)^{2}

= 49 (21 a + 11)^{2} (3 a + 1)^{2}

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