Getal & Ruimte (13e editie) - 2 vwo
'Ontbinden in factoren'.
| 2 vwo | 7.1 Buiten haakjes brengen |
opgave 1Ontbind 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 2Ontbind 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 3Ontbind 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 4Ontbind 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 5Ontbind 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 |
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| 2 vwo | 7.2 De product-som methode |
opgave 1Ontbind 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 2Ontbind 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 |