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

\(a^{2} + a\)

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

a

\(a^{2} + a = a (a + 1)\)

1p

1p

b

\(15 a^{2} + 21 a\)

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

b

\(15 a^{2} + 21 a = 3 a (5 a + 7)\)

1p

1p

c

\(9 x y + 15 x\)

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

c

\(9 x y + 15 x = 3 x (3 y + 5)\)

1p

1p

d

\(15 p q + 24 p r\)

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

d

\(15 p q + 24 p r = 3 p (5 q + 8 r)\)

1p

opgave 2

Ontbind in factoren.

1p

a

\(8 x y z + 10 x y\)

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

a

\(8 x y z + 10 x y = 2 x y (4 z + 5)\)

1p

1p

b

\(10 a^{4} + 45 a^{5}\)

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

b

\(10 a^{4} + 45 a^{5} = 5 a^{4} (2 + 9 a)\)

1p

1p

c

\(2 x^{7} - 7 x^{8} + x\)

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

c

\(2 x^{7} - 7 x^{8} + x = x (2 x^{6} - 7 x^{7} + 1)\)

1p

1p

d

\(18 x^{5} y^{2} + 21 x^{2} y^{3}\)

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

d

\(18 x^{5} y^{2} + 21 x^{2} y^{3} = 3 x^{2} y^{2} (6 x^{3} + 7 y)\)

1p

opgave 3

Ontbind in factoren.

1p

a

\(a^{2} - 81\)

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

a

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

1p

1p

b

\(49 p^{2} - 4\)

Verschil2Kwadraten (2)
00hm - Ontbinden in factoren - basis - 1ms - dynamic variables

b

\(49 p^{2} - 4 = (7 p - 2) (7 p + 2)\)

1p

1p

c

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

Verschil2Kwadraten (3)
00hs - Ontbinden in factoren - basis - 1ms - dynamic variables

c

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

1p

1p

d

\(16 p^{8} - 25\)

Verschil2Kwadraten (4)
00ht - Ontbinden in factoren - basis - 1ms - dynamic variables

d

\(16 p^{8} - 25 = (4 p^{4} - 5) (4 p^{4} + 5)\)

1p

opgave 4

Ontbind in factoren.

1p

a

\(16 a^{2} - 4\)

Verschil2Kwadraten (5)
00hu - Ontbinden in factoren - basis - 1ms - dynamic variables

a

\(16 a^{2} - 4 = 4 (4 a^{2} - 1) = 4 (2 a - 1) (2 a + 1)\)

1p

1p

b

\(75 x^{3} - 48 x\)

Verschil2Kwadraten (6)
00hv - Ontbinden in factoren - basis - 1ms - dynamic variables

b

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

1p

1p

c

\(x^{12} - 81\)

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

c

\(x^{12} - 81 = (x^{6} - 9) (x^{6} + 9) = (x^{3} - 3) (x^{3} + 3) (x^{6} + 9)\)

1p

1p

d

\(2 x^{13} - 32 x\)

Verschil2Kwadraten (8)
00hx - Ontbinden in factoren - basis - 1ms - dynamic variables

d

\(2 x^{13} - 32 x = 2 x (x^{12} - 16) = 2 x (x^{6} - 4) (x^{6} + 4) = 2 x (x^{3} - 2) (x^{3} + 2) (x^{6} + 4)\)

1p

opgave 5

Ontbind in factoren.

1p

\(p^{12} q^{12} - 9 r^{10}\)

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

\(p^{12} q^{12} - 9 r^{10} = (p^{6} q^{6} - 3 r^{5}) (p^{6} q^{6} + 3 r^{5})\)

1p

2 vwo 7.2 De product-som methode

Ontbinden in factoren (6)

opgave 1

Ontbind in factoren.

1p

a

\(a^{2} + 13 a + 36\)

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

a

\(a^{2} + 13 a + 36 = (a + 9) (a + 4)\)

1p

1p

b

\(x^{2} - 4 x - 45\)

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

b

\(x^{2} - 4 x - 45 = (x - 9) (x + 5)\)

1p

1p

c

\(a^{2} - 12 a + 32\)

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

c

\(a^{2} - 12 a + 32 = (a - 8) (a - 4)\)

1p

1p

d

\(x^{2} - 8 x + 16\)

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

d

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

1p

opgave 2

Ontbind in factoren.

1p

a

\(4 p^{5} + 20 p^{4} + 16 p^{3}\)

SomProductmethode (5)
00hr - Ontbinden in factoren - basis - 1ms - dynamic variables

a

\(4 p^{5} + 20 p^{4} + 16 p^{3} = 4 p^{3} (p^{2} + 5 p + 4) = 4 p^{3} (p + 4) (p + 1)\)

1p

1p

b

\(a^{4} - 17 a^{2} + 72\)

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

b

\(a^{4} - 17 a^{2} + 72 = (a^{2} - 8) (a^{2} - 9)\)

1p

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