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117 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Wat is een Term?
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Term: iets wat je optelt of aftrekt in een formule.
in de vergelijking 3q -7 zijn 3q en 7 termen. De worden van elkaar afgetrokken. |
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Wat is een Factor?
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Factor: iets wat je vermenigvuldigt in een formule.
5 en 3q – 7 zijn factoren. Die worden met elkaar vermenigvuldigd. |
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Hoe luidt de merkwaardige product: Kwadraat van Som?
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Dus:
(a + b)² = a²+ 2ab + b² |
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Hoe luidt de merkwaardige product: Kwadraat van Verschil?
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(a – b)² = a² – 2ab + b²
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Hoe luidt de merkwaardige product: Verschil van Kwadraten?
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a² - b² = (a + b) (a - b)
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wat zijn de factors van:
x² + 4x - 21 = 0 |
x² + 4x - 21 = 0
(x + 7) (x - 3) = 0 |
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wat zijn de factors van:
x² - 5x + 6 = 0 |
x² - 5x + 6 = 0
(x - 6) (x + 1) = 0 |
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wat zijn de factors van:
x² - x - 6 = 0 |
x² - x - 6 = 0
(x - 3) (x + 2) = 0 |
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wat zijn de factors van:
x² + 5x - 14 = 0 |
x² + 5x - 14 = 0
(x + 7) (x - 2) = 0 |
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wat zijn de factors van:
x² + x - 20 = 0 |
x² + x - 20 = 0
(x + 5) (x - 4) = 0 |
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wat zijn de factors van:
x² - x = 42 |
x² - x - 42 = 0
(x - 7) (x + 6) = 0 |
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wat zijn de factors van:
x² + 12x - 35 = 0 |
x² + 12 x - 35 = 0
(x - 7) (x - 5) = 0 |
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wat zijn de factors van:
x² + 10x = - 21 |
x² + 10x = -21
x² + 10x + 21 = 0 (x + 7) (x - 3) = 0 |
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wat zijn de factors van:
x² - x - 6 = 0 |
x² - x - 6 = 0
(x - 3) (x + 2) = 0 |
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wat zijn de factors van:
x² + 3 = 4 |
x²+ 3x = 4
x² + 3x - 4 = 0 (x - 4) (x + 1) = 0 |
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wat zijn de factors van:
x² + 2x - 15 = 0 |
x² + 2x - 15 = 0
(x + 5) (x - 3) = 0 |
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Los op:
y² - 9x + 20 = 0 |
y² - 9x + 20 = 0
(y - 10) (y + 1) = 0 |
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Los op:
p² + 2q - 35 = 0 |
p² + 2q - 35 = 0
(p + 7) (p - 2) = 0 |
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Los op:
3a² + 12a = 0 |
3a² + 12a = 0
3a (a + 12) = 0 |
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Los op:
x² - 12 + x = 0 |
x² - 12 + x = 0
x² + x - 12 = 0 (x + 4) (x - 3) = 0 |
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Los op:
5t - t² = 0 |
5t - t² = 0
-t² + 5t = 0 t( -t + 5) = 0 t = 0 of t = 5 |
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Los op:
63 + q² - 16q = 0 |
63 + q² - 16q = 0
q² - 16 q + 63 = 0 (q - 9) (q + 7) = 0 |
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Los op:
x² - 7x = 18 |
x² - 7x = 18
x² - 7x - 18 = 0 (x - 9) (x + 2) = 0 |
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Los op:
x² - 7x = 2x |
x² - 7x = 2x
x² - 7x - 2x = 0 x² - 9x = 0 x (x - 9) = 0 |
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Los op:
3x² + 15x = 18 |
3x² + 15x = 18
3x² + 15x - 18 = 0 -> delen 3 x² + 5x - 6 = 0 (x - 3) (x + 2) = 0 |
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Los op:
(x + 4)² = 16x |
(x + 4)² = 16x
-> Toepassing merkwaardig product x² + 8x + 16 = 16x x² - 8x + 16 = 0 weer een merkwaardig product maar nu anders om (x - 4)² = 0 x = 4 |
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Ontbind in factoren:
3ab + 9a |
3ab + 9a =
3a (b + 3) |
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Ontbind in factoren:
12ab - 9b |
12ab - 9b =
3b (4a - 3) |
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Ontbind in factoren:
3² + 6a |
3²+ 6a =
3a (a + 2) |
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Ontbind in factoren:
3a² - 6b |
3a² - 6b =
3 (a² - 2b) = 3 (a + V2b) (a - V2b) *V = wortel van |
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Ontbind in factoren:
3ab - 3a |
3ab - 3a =
3a (b - 1) |
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Ontbind in factoren:
3ab - 9ac |
3ab - 9ac =
3a (b - 3c) |
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Ontbind in factoren:
12xyz - 16xy |
12xyz - 16xy =
4xy (3z - 4) |
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Ontbind in factoren:
2xy + 8xz |
2xy + 8xz =
2x (y + 4z) |
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Ontbind in factoren:
5x² - 15x^3 |
5x² - 15x^3 =
5x²(1 - 3x) |
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Ontbind in factoren:
6x³ - 12x |
6x³ - 12x =
6x (x² - 2) = 6x (x + V2) (x - V2) *V de wortel van |
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Ontbind in factoren:
25x² - 30x |
25x² - 30x =
5x ( 5x - 6 ) |
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Ontbind in factoren:
10x² + 5x²y |
10x² + 5x²y =
5x² (2 + y) |
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Ontbind in factoren:
6x⁴ - 3x² |
6x⁴ - 3x² =
3x² (x² - 1) = 3x² (x + 1) (x - 1) |
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Ontbind in factoren:
18a²bc + 12ab²c |
18a²bc + 12ab²c =
6abc (3a + 2b) |
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Ontbind in factoren:
x⁴ - x³ + x² = |
x⁴ - x³ + x² =
x²(x² - x + 1) |
alt + 252 = superscript ³
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Ontbind in zoveel mogelijk factoren:
4x²y + xy – xy² = |
4x²y + xy – xy² =
xy (4x + 1 - y) |
alt+253 superscript ²
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Ontbind in zoveel mogelijk factoren:
12x⁸ + 18x⁶ + 16x⁵ |
12x⁸+ 18x⁶+ 16x⁵ =
2x⁵(6x³ + 9x + 8) |
³ ⁵ ⁶
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Ontbind in zoveel mogelijk factoren:
9p²q²r - 6p²r³ |
9p²q²2r - 6pq²r³ =
3pqr(3pq - 2qr²) |
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Ontbind in zoveel mogelijk factoren:
9x² - 16 |
9x² - 16 =
(3x)² - 4²= (3x - 4)(3x + 4) |
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Ontbind in zoveel mogelijk factoren:
25a² - 4 |
25a² - 4 =
(5a)² - 2² = (5a + 2)(5a - 2) |
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Ontbind in zoveel mogelijke termen:
36a² - 121 |
36a² - 121 =
(6a)² - 11² = -> toepassing: a² - b² = (a + b)(a - b) => (6a + 11)(6a - 11) |
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Ontbind in zoveel mogelijke termen:
a² - 64 |
a² - 64 =
a² - 8² = -> toepassing: a² - b² = (a + b)(a - b) => (a + 8)(a - 8) |
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Ontbind in zoveel mogelijke termen:
36a² - a |
36a² - a =
a(36a - 1) |
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Ontbind in zoveel mogelijke termen:
a² - 64a |
a² - 64a =
a(a - 64) = a((Va)² - 8²) = -> toepassing: a² - b² = (a + b)(a - b) => a(Va + 8)(Va - 8) |
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Ontbind in zoveel mogelijke termen:
225a² - 0,01 |
225a² - 0,01 =
(15a)² - (0,1)² = -> toepassing: a² - b² = (a + b)(a - b) => (15a - 0,1)(15a + 0,1) |
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Ontbind in zoveel mogelijke factoren:
x³ - 16x |
x³ - 16x =
x(x² - 16) = x(x² - 4²) = x(x + 4)(x - 4) |
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Ontbind in zoveel mogelijke factoren:
x³ - 64x² |
x³ - 64x² =
x²(x - 64) |
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Ontbind in zoveel mogelijke factoren:
x³ - 64x |
x³ - 64x =
x(x² - 64) = x(x² - 8²) = x(x + 8)(x - 8) |
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Ontbind in zoveel mogelijke factoren:
x⁴ - 16x² |
x⁴ - 16x² =
x²(x² - 16) = x²(x² - 4²) = x²(x + 4)(x - 4) |
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Ontbind in zoveel mogelijke factoren:
x⁴ + 16x² |
x⁴ + 16x² =
x²(x² + 16) |
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Ontbind in zoveel mogelijk factoren:
x⁴ + 16x³ |
x⁴ + 16x³ =
x³(x + 16) |
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Ontbind in zoveel mogelijk factoren:
5p² - 125 |
5p² - 125 =
5(p² - 25) = 5(p² - 5²) = 5(p + 5)(p - 5) |
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Ontbind in zoveel mogelijk factoren:
x⁴ - 16 |
x⁴ - 16 =
(x²)² - (4)² = (x² + 4)(x² - 4) = (x² + 4)(x² - 2²) = (x² + 4)(x + 2)(x - 2) |
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Ontbind in zoveel mogelijk factoren:
a¹⁰ - 9 |
a¹⁰ - 9 =
(a⁵)² - (3)² = (a⁵ + 3)(a⁵ - 3) |
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Ontbind in zoveel mogelijk factoren:
q⁸ + p⁶q⁶ |
q⁸ + p⁶q⁶ =
q⁶(q² + p⁶) |
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Ontbind in zoveel mogelijke factoren:
x⁸y⁶ - z² |
x⁸y⁶ - z² =
(x⁴y³)² - (z)² = (x⁴y³ + z)(x⁴y³ - z) |
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Ontbind in zoveel mogelijke factoren:
18k⁸ - 18 |
18k⁸ - 18 =
18(k⁸ - 1) = 18((k⁴)² - (1)²) = 18(k⁴ + 1)(k⁴ - 1)= 18(k⁴ + 1)((k²)² - (1)²)= 18(k⁴ + 1)(k² + 1)(k² - 1) = 18(k⁴ + 1)(k² + 1)(k + 1)(k - 1) |
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Ontbind in zoveel mogelijke factoren:
x³ - 2x² - 8x |
x³ - 2x² - 8x =
x(x² - 2x - 8) = x(x - 4)(x + 2) |
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Ontbind in zoveel mogelijke factoren:
5x³ - 10x² - 15x |
5x³ - 10x² - 15x =
5x(x² - 2x - 3) = 5x(x - 3)(x +1) |
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Ontbind in zoveel mogelijke factoren:
x⁴ - x³ - x² |
x⁴ - x³ - x² =
x²(x² - x - 1) |
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ontbind in factoren
x³ - 64x |
x³ - 64x =
x(x² - 64) = x(x² - 8² ) = x(x + 8)(x - 8) |
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ontbind in factoren
6x² - 6x - 18 |
6x² - 6x - 18 =
6(x² - x - 3) = 6(x - 3)(x + 1) |
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ontbind in factoren
x³y² + 2x³y - 15x³ |
x³y² + 2x³y - 15x³ =
x³(y² + 2y - 3) = x³(y + 3)(y - 1) |
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ontbind in factoren
x² - 17x - 60 |
x² - 17x - 60 =
(x - 20)(x + 3) |
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ontbind in factoren
x² + 15x + 50 |
x² + 15x + 50 =
(x + 10)(x + 5) |
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ontbind in factoren
x² + 18x - 63 |
x² + 18x - 63 =
(x + 21)(x - 3) |
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ontbind in factoren
x³ - 7x² - 30x |
x³ - 7x² - 30x =
x(x² - 7x - 30) = x(x -10)(x +3) |
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ontbind in factoren
x² + 16x |
x² + 16x =
x(x + 16) |
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ontbind in factoren
68 - 21x + x² |
68 - 21x + x² =
x² - 21x + 68 = (x -17)(x - 4) |
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ontbind in factoren
6x² - 32x |
6x² - 32x =
x(6x - 32) |
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ontbind in factoren
16x⁵ - x³ |
16x⁵ - x³ =
x³(16x² - 1) = x³((4x)² - 1) = x³(4x + 1)(4x - 1) |
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ontbind in factoren
x² - 56 - x |
x² - 56 - x =
x² - x - 56 = (x - 8)(x + 7) |
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los op
(x + 3)(x - 9) = 0 |
(x + 3)(x - 9) = 0
x = -3 ∨ x = 9 |
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los op
2x(x + 5) = 0 |
2x(x + 5) = 0
2x = 0 ∨ x + 5 = 0 x = 0 ∨ x - 5 |
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los op
(x - 1)(2x + 15) = 0 |
(x - 1)(2x + 15) = 0
x - 1 = 0 ∨ 2x + 15 = 0 x = 1 ∨ 2x = -15 x = 1 ∨ x = -7,5 |
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los op
a(0,5a - 10) = 0 |
a(0,5a - 10) = 0
a = 0 ∨ (0,5a - 10) = 0 a = 0 ∨ a = 20 |
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los op
(x + 3)(x - 3) = 0 |
(x + 3)(x - 3) = 0
x + 3 = 0 ∨ x - 3 = 0 x = -3 ∨ x = 3 |
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los op
(2a - 5)(2a - 5) = 0 |
(2a - 5)(2a - 5) = 0
2a - 5 = 0 a = 2,5 |
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los op
x(x + 3) = 0 |
x(x + 3) = 0
x = 0 ∨ x + 3 = 0 x = 0 ∨ x = -3 |
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los op
5a(2a + 7) = 0 |
5a(2a + 7) = 0
5a = 0 ∨ 2a + 7 = 0 a = 0 ∨ a = -3,5 |
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los op
x² + 7x + 12 = 0 |
x² + 7x + 12 = 0
(x + 4)(x + 3) = 0 x + 4 = 0 ∨ x + 3 = 0 x = -4 ∨ x = -3 |
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los op
a² - a - 12 = 0 |
a² - a - 12 = 0
(a - 4)(a + 3) = 0 a - 4 = 0 ∨ a + 3 = 0 a = 4 ∨ a = -3 |
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los op
a² - 10a - 24 = 0 |
a² - 10a - 24 = 0
(a - 6)(a - 4) = 0 a - 6 = 0 ∨ a - 4 = 0 a = 6 ∨ a = 4 |
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los op
x² - 10x + 24 = 0 |
x² - 10x - 24 = 0
(x - 12)(x + 2) = 0 x - 12 = 0 ∨ x + 2 = 0 x = 12 ∨ x = -2 |
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los op
x² - 25 = 0 |
x² - 25 = 0
x² = 25 x = √25 ∨ x = -√25 x = 5 ∨ x = -5 |
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los op
25x² - 16 = 0 |
25x² - 16 = 0
(5x)² - 4² = 0 5x + 4 = 0 ∨ 5x - 4 = 0 x = -4/5 ∨ x = 4/5 |
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los op
16x² - x = 0 |
16x² - x = 0
x(16x - 1) = 0 x = 0 ∨ 16x - 1 = 0 x = 0 ∨ x = 1/16 |
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los op
9x² - 49 = 0 |
9x² - 49 = 0
(3x)² - 7² = 0 3x - 7 = 0 ∨ 3x + 7 = 0 x = 7/3 ∨ x = -7/3 x = 2,333 ∨ x = -2,333 |
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los op
x² - 121 = 0 |
x² - 121 = 0
x² - 11² = 0 x + 11 = 0 ∨ x - 11 = 0 x = -11 ∨ x = 11 |
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los op
16x² + 81x = 0 |
16x² - 81x = 0
x(16x - 81) = 0 x = 0 ∨ 16x - 81 = 0 x = 0 ∨ x = 81/16 etc |
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los op
y² - 9y + 20 = 0 |
y² - 9y + 20 = 0
(y - 5)(y - 4) = 0 y - 5 = 0 ∨ y - 4 = 0 y = 5 ∨ y = 4 |
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los op
p² + 2p - 35 = 0 |
p² + 2p - 35 = 0
(p + 7)(p - 5) = 0 p + 7 =0 ∨ p - 5 = 0 p = -7 ∨ p = 5 |
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los op
3a² + 12a = 0 |
3a² + 12a = 0
3a(a + 4) = 0 3a = 0 ∨ a + 4 = 0 a = 0 ∨ a = -4 |
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los op
x² - 12 + x = 0 |
x² - 12 + x = 0
x² + x - 12 = 0 (x + 4)(x - 3) = 0 x + 4 = 0 ∨ x - 3 = 0 x = -4 ∨ x = 3 |
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los op:
5t - t² = 0 |
5t - t² = 0
t(5 - t) = 0 t = 0 ∨ 5 - t = 0 t = 0 ∨ t = 5 |
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los op:
63 + q² + 16q = 0 |
63 + q² + 16q = 0
q² + 16q + 63 = 0 (q +9)(q +7) = 0 q + 9 = 0 ∨ q + 7 = 0 q = -9 ∨ q = -7 |
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los op:
x² + 3x = 10 |
x² + 3x = 10
x² + 3x -10 = 10 - 10 x² + 3x -10 = 0 (x - 5)(x + 2) = 0 x - 5 = 0 ∨ x + 2 = 0 x = 5 ∨ x = -2 |
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los op:
x² -x = 12 |
x² -x = 12
x² -x -12 = 12 - 12 x² -x -12 = 0 (x - 4)(x + 3) = 0 x - 4 = 0 ∨ x + 3 = 0 x = 4 ∨ x = -3 |
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los op:
x² = 5x |
x² = 5x
x² - 5x = 5x - 5x x² - 5x = 0 x(x - 5) = 0 x = 0 ∨ x - 5 = 0 x = 0 ∨ x = 5 |
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los op:
x² - 5 = 4x |
x² - 5 = 4x
x² - 5 - 4x = 4x - 4x x² - 5 - 4x = 0 x² - 4x - 5 = 0 (x - 5)(x + 1) = 0 x - 5 = 0 ∨ x + 1 = 0 x = 5 ∨ x = -1 |
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los op:
x² + 18 = 19x |
x² + 18 = 19x
x² + 18 - 19x = 19x - 19x x² + 18 - 19x = 0 x² - 19x + 18 = 0 (x - 19)(x + 1) = 0 x - 19 = 0 ∨ x + 1 = 0 x = 19 ∨ x = -1 |
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los op:
x² - 3x = 18 |
x² - 3x = 18
x² - 3x -18 = 18 - 18 x² - 3x - 18 = 0 (x - 6)(x + 3) = 0 x - 6 = 0 ∨ x + 3 = 0 x = 6 ∨ x = -3 |
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los op:
x² + 3x = 5x |
x² + 3x = 5x
x² + 3x - 5x = 5x - 5x x² - 2x = 0 x(x - 2) = 0 x = 0 ∨ x - 2 = 0 x = 0 ∨ x = 2 |
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los op:
x² + 4 = 9x - 4 |
x² + 4 = 9x - 4
x² + 4 + 4 = 9x - 4 + 4 x² + 8 = 9x x² + 8 - 9x = 9x - 9x x² + 8 - 9x = 0 x² - 9x + 8 = 0 (x - 9)(x + 1) = 0 x - 9 = 0 ∨ x + 1 = 0 x = 9 ∨ x = -1 |
∨∨
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los op:
3x(x - 1) = 0 |
3x(x - 1) = 0
3x = 0 ∨ x -1 = 0 x = 0 ∨ x = 1 |
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los op:
x² = x + 2 |
x² = x + 2
x² -x - 2 = x - x + 2 - 2 x² - x - 2 = 0 (x - 2)(x + 1) = 0 x - 2 = 0 ∨ x + 1 = 0 x = 2 ∨ x = -1 |
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los op:
x² + 5x + 6 = 6 |
x² + 5x + 6 = 6
x² + 5x + 6 - 6 = 6 - 6 x² + 5x = 0 x(x + 5) = 0 x = 0 ∨ x + 5 = 0 x = 0 ∨ x = -5 |
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los op:
x² + 3x + 1 = 29 |
x² + 3x + 1 = 29
x² + 3x + 1 - 29 = 29 - 29 x² + 3x - 28 = 0 (x + 7)(x - 4) = 0 x + 7 = 0 ∨ x - 4 = 0 x = -7 ∨ x = -4 |
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los op:
x² - 7x = 0 |
x² - 7x = 0
x(x - 7) = 0 x = 0 ∨ x - 7 = 0 x = 0 ∨ x = 7 |
∨∨
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los op:
x² - 7x = 2x |
x² - 7x = 2x
x² - 7x - 2x = 2x - 2x x² - 9x = 0 x(x - 9) = 0 x = 0 ∨ x - 9 = 0 x = 0 ∨ x = 9 |
∨∨
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los op:
x² - 7x = 0 |
x² - 7x = 0
x(x - 7) = 0 x = 0 ∨ x - 7 = 0 x = 0 ∨ x = 7 |
∨∨
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