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

\(x^{2} + 5 x\)

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

a

\(x^{2} + 5 x = x (x + 5)\)

1p

1p

b

\(25 p^{2} + 45 p\)

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

b

\(25 p^{2} + 45 p = 5 p (5 p + 9)\)

1p

1p

c

\(9 a b + 24 a\)

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

c

\(9 a b + 24 a = 3 a (3 b + 8)\)

1p

1p

d

\(15 a b + 24 a c\)

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

d

\(15 a b + 24 a c = 3 a (5 b + 8 c)\)

1p

opgave 2

Ontbind in factoren.

1p

a

\(12 x y z + 16 x y\)

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

a

\(12 x y z + 16 x y = 4 x y (3 z + 4)\)

1p

1p

b

\(12 x^{5} + 14 x^{2}\)

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

b

\(12 x^{5} + 14 x^{2} = 2 x^{2} (6 x^{3} + 7)\)

1p

1p

c

\(2 a + 5 a^{4} + a^{6}\)

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

c

\(2 a + 5 a^{4} + a^{6} = a (2 + 5 a^{3} + a^{5})\)

1p

1p

d

\(14 p^{4} q^{3} + 18 p^{5} q^{4}\)

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

d

\(14 p^{4} q^{3} + 18 p^{5} q^{4} = 2 p^{4} q^{3} (7 + 9 p q)\)

1p

opgave 3

Ontbind in factoren.

1p

a

\(x^{2} - 64\)

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

a

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

1p

1p

b

\(81 a^{2} - 4\)

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

b

\(81 a^{2} - 4 = (9 a - 2) (9 a + 2)\)

1p

1p

c

\(81 - 16 x^{2}\)

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

c

\(81 - 16 x^{2} = (9 - 4 x) (9 + 4 x)\)

1p

1p

d

\(81 p^{8} - 49\)

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

d

\(81 p^{8} - 49 = (9 p^{4} - 7) (9 p^{4} + 7)\)

1p

opgave 4

Ontbind in factoren.

1p

a

\(75 a^{2} - 48\)

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

a

\(75 a^{2} - 48 = 3 (25 a^{2} - 16) = 3 (5 a - 4) (5 a + 4)\)

1p

1p

b

\(5 a^{5} - 20 a^{3}\)

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

b

\(5 a^{5} - 20 a^{3} = 5 a^{3} (a^{2} - 4) = 5 a^{3} (a - 2) (a + 2)\)

1p

1p

c

\(x^{4} - 16\)

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

c

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

1p

1p

d

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

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

d

\(x^{6} - x^{2} = x^{2} (x^{4} - 1) = x^{2} (x^{2} - 1) (x^{2} + 1) = x^{2} (x - 1) (x + 1) (x^{2} + 1)\)

1p

opgave 5

Ontbind in factoren.

1p

\(x^{6} y^{10} - 4 z^{8}\)

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

○

\(x^{6} y^{10} - 4 z^{8} = (x^{3} y^{5} - 2 z^{4}) (x^{3} y^{5} + 2 z^{4})\)

1p
2 vwo 7.2 De product-som methode

Ontbinden in factoren (6)

opgave 1

Ontbind in factoren.

1p

a

\(a^{2} + 11 a + 18\)

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

a

\(a^{2} + 11 a + 18 = (a + 2) (a + 9)\)

1p

1p

b

\(p^{2} - 6 p - 7\)

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

b

\(p^{2} - 6 p - 7 = (p - 7) (p + 1)\)

1p

1p

c

\(a^{2} - 6 a + 8\)

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

c

\(a^{2} - 6 a + 8 = (a - 4) (a - 2)\)

1p

1p

d

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

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

d

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

1p

opgave 2

Ontbind in factoren.

1p

a

\(3 x^{4} + 36 x^{3} + 105 x^{2}\)

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

a

\(3 x^{4} + 36 x^{3} + 105 x^{2} = 3 x^{2} (x^{2} + 12 x + 35) = 3 x^{2} (x + 5) (x + 7)\)

1p

1p

b

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

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

b

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

1p
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