Getal & Ruimte (13e editie) - 2 vwo

'Ontbinden in factoren'.

2 vwo 7.1 Buiten haakjes brengen

Ontbinden in factoren (17)

opgave 1

Ontbind in factoren.

1p

a

\(p^{2} + 4 p\)

BuitenHaakjes (1)
00hd - Ontbinden in factoren - basis - 0ms - dynamic variables

a

\(p^{2} + 4 p = p (p + 4)\)

1p

1p

b

\(4 a^{2} - 10 a\)

BuitenHaakjes (2)
00he - Ontbinden in factoren - basis - 0ms - dynamic variables

b

\(4 a^{2} - 10 a = 2 a (2 a - 5)\)

1p

1p

c

\(25 a b + 35 a\)

BuitenHaakjes (3)
00hf - Ontbinden in factoren - basis - 0ms - dynamic variables

c

\(25 a b + 35 a = 5 a (5 b + 7)\)

1p

1p

d

\(6 x y + 9 x z\)

BuitenHaakjes (4)
00hg - Ontbinden in factoren - basis - 0ms - dynamic variables

d

\(6 x y + 9 x z = 3 x (2 y + 3 z)\)

1p

opgave 2

Ontbind in factoren.

1p

a

\(25 x y z + 35 x y\)

BuitenHaakjes (5)
00hh - Ontbinden in factoren - basis - 0ms - dynamic variables

a

\(25 x y z + 35 x y = 5 x y (5 z + 7)\)

1p

1p

b

\(24 a^{3} - 27 a^{5}\)

BuitenHaakjes (6)
00hi - Ontbinden in factoren - basis - 0ms - dynamic variables

b

\(24 a^{3} - 27 a^{5} = 3 a^{3} (8 - 9 a^{2})\)

1p

1p

c

\(5 x + 6 x^{7} + x^{3}\)

BuitenHaakjes (7)
00hj - Ontbinden in factoren - basis - 0ms - dynamic variables

c

\(5 x + 6 x^{7} + x^{3} = x (5 + 6 x^{6} + x^{2})\)

1p

1p

d

\(25 a b + 35 a^{3} b^{2}\)

BuitenHaakjes (8)
00hk - Ontbinden in factoren - basis - 0ms - dynamic variables

d

\(25 a b + 35 a^{3} b^{2} = 5 a b (5 + 7 a^{2} b)\)

1p

opgave 3

Ontbind in factoren.

1p

a

\(p^{2} - 9\)

Verschil2Kwadraten (1)
00hl - Ontbinden in factoren - basis - 0ms - dynamic variables

a

\(p^{2} - 9 = (p - 3) (p + 3)\)

1p

1p

b

\(25 x^{2} - 64\)

Verschil2Kwadraten (2)
00hm - Ontbinden in factoren - basis - 0ms - dynamic variables

b

\(25 x^{2} - 64 = (5 x - 8) (5 x + 8)\)

1p

1p

c

\(4 - 25 a^{2}\)

Verschil2Kwadraten (3)
00hs - Ontbinden in factoren - basis - 0ms - dynamic variables

c

\(4 - 25 a^{2} = (2 - 5 a) (2 + 5 a)\)

1p

1p

d

\(100 x^{8} - 49\)

Verschil2Kwadraten (4)
00ht - Ontbinden in factoren - basis - 0ms - dynamic variables

d

\(100 x^{8} - 49 = (10 x^{4} - 7) (10 x^{4} + 7)\)

1p

opgave 4

Ontbind in factoren.

1p

a

\(100 x^{2} - 16\)

Verschil2Kwadraten (5)
00hu - Ontbinden in factoren - basis - 0ms - dynamic variables

a

\(100 x^{2} - 16 = 4 (25 x^{2} - 4) = 4 (5 x - 2) (5 x + 2)\)

1p

1p

b

\(5 a^{3} - 80 a\)

Verschil2Kwadraten (6)
00hv - Ontbinden in factoren - basis - 0ms - dynamic variables

b

\(5 a^{3} - 80 a = 5 a (a^{2} - 16) = 5 a (a - 4) (a + 4)\)

1p

1p

c

\(p^{8} - 16\)

Verschil2Kwadraten (7)
00hw - Ontbinden in factoren - basis - 0ms - dynamic variables

c

\(p^{8} - 16 = (p^{4} - 4) (p^{4} + 4) = (p^{2} - 2) (p^{2} + 2) (p^{4} + 4)\)

1p

1p

d

\(p^{10} - 81 p^{2}\)

Verschil2Kwadraten (8)
00hx - Ontbinden in factoren - basis - 0ms - dynamic variables

d

\(p^{10} - 81 p^{2} = p^{2} (p^{8} - 81) = p^{2} (p^{4} - 9) (p^{4} + 9) = p^{2} (p^{2} - 3) (p^{2} + 3) (p^{4} + 9)\)

1p

opgave 5

Ontbind in factoren.

1p

\(a^{12} b^{2} - 64 c^{6}\)

Verschil2Kwadraten (9)
00hz - Ontbinden in factoren - basis - 0ms - dynamic variables

○

\(a^{12} b^{2} - 64 c^{6} = (a^{6} b - 8 c^{3}) (a^{6} b + 8 c^{3})\)

1p
2 vwo 7.2 De product-som methode

Ontbinden in factoren (6)

opgave 1

Ontbind in factoren.

1p

a

\(a^{2} + 11 a + 24\)

SomProductmethode (1)
00hn - Ontbinden in factoren - basis - 0ms - dynamic variables

a

\(a^{2} + 11 a + 24 = (a + 8) (a + 3)\)

1p

1p

b

\(x^{2} + 4 x - 12\)

SomProductmethode (2)
00ho - Ontbinden in factoren - basis - 0ms - dynamic variables

b

\(x^{2} + 4 x - 12 = (x - 2) (x + 6)\)

1p

1p

c

\(x^{2} - 17 x + 72\)

SomProductmethode (3)
00hp - Ontbinden in factoren - basis - 0ms - dynamic variables

c

\(x^{2} - 17 x + 72 = (x - 8) (x - 9)\)

1p

1p

d

\(p^{2} + 18 p + 81\)

SomProductmethode (4)
00hq - Ontbinden in factoren - basis - 0ms - dynamic variables

d

\(p^{2} + 18 p + 81 = (p + 9) (p + 9)\)

1p

opgave 2

Ontbind in factoren.

1p

a

\(2 a^{3} - 20 a^{2} + 48 a\)

SomProductmethode (5)
00hr - Ontbinden in factoren - basis - 0ms - dynamic variables

a

\(2 a^{3} - 20 a^{2} + 48 a = 2 a (a^{2} - 10 a + 24) = 2 a (a - 6) (a - 4)\)

1p

1p

b

\(x^{6} - x^{3} - 56\)

SomProductmethode (6)
00hy - Ontbinden in factoren - basis - 0ms - dynamic variables

b

\(x^{6} - x^{3} - 56 = (x^{3} + 7) (x^{3} - 8)\)

1p
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