Wiskunde.net

1.
a.
oppervlakte(rechthoek I) = 3 x a = 3a
oppervlakte(rechthoek II) = 3 x b = 3b
b.
oppervlakte(ABCD) = oppervlakte(rechthoek I) + oppervlakte(rechthoek II)
oppervlakte(ABCD) = 3a + 3b
Dus 3(a + b) = 3a + 3b

2.
a. -3a + 6b
b. 3p² - 6p
c. -24ab + 36c
d. 15x² - 10x
e. -x² - y
f. -4m + 2n

3.
a. 6a + 12b + 2a + 6b = 8a + 18b
b. 10x - 40 + 4x - 8 = 14x - 48
c. -2x - 12y + 6x + 9y = 4x - 3y
d. -p + 5q + 2p - 8q = p - 3q
e. 8 - 20a - 12 + 10 = -20a + 6
f. -6a + 10b + 10b + 2a = -4a + 20b
g. -x² - xy - 2x + 2xy = -x² + xy - 2x
h. 6p² - 12p - 6p² - 8p = -20p

4.
a. -4x - 35x + 10y = -39x + 10y
b. 5a - 8a + 32 = -3a + 32
c. a + b - 4a + 2b = -3a + 3b
d. -8a - 16b - 15a + 10b = -23a - 6b
e. -3x + 12y - x + 2y - 13y = -4x + y
f. -2a² + 2ab + ab - 3a² - 3ab = -5a²

5.
a. 3(x - 5) = 3x - 15
b. 3(a + 5) - 2a
= 3a + 15 - 2a
= a + 15

6.
a. 10a + 40 - 2a - 6 = 8a + 34
b. oppervlakte blauw: 3(x + 5) = 3x + 15
oppervlakte geel: 9(2a - 1) - 3 x 5 = 18a - 9 - 15 = 18a - 24
oppervlakte paars: 8(3p + 5) - 4(2p + 1) = 24p + 40 - 8p - 4 = 16p + 36

7.
*

8.
a. 6ax + 18ay - 3az - 6ax + 12xy - 6xz - 18ay - 12xy - 6yz = -3az - 6xz - 6yz
b. 12ax - 8bx - 2cx - 12ax - ab + 2ac - bc + 8bx + ab = -2cx + 2ac - bc
c. 2a² - 3ab + 4ab + 6b² - 2a² - 3ab - 4ab + 6b² = -6ab + 12b²

9.
a.
oppervlakte trapezium = 1/2 ⋅ (a + b) ⋅ h
= 1/2 ⋅ (CD + AB) ⋅ a
= 1/2 ⋅ ( (2a-5) + (2a+3) ) ⋅ a
= 1/2 ⋅ (4a - 2) ⋅ a
= (2a - 1) ⋅ a
= 2a² - a
b.
oppervlakte vlieger = 1/2 ⋅ korte diagonaal ⋅ lange diagonaal
= 1/2 ⋅ (1/2a + 1/2a) ⋅ ( (a-1) + (a+5) )
= 1/2 ⋅ a ⋅ (2a + 4)
= 1/2a ⋅ (2a + 4)
= a² + 2a
c.
oppervlakte trapezium = 1/2 ⋅ (a + b) ⋅ h
= 1/2 ⋅ (NM + KL) ⋅ 4a
= 1/2 ⋅ ( (4a+2) + (5a+6) ) ⋅ 4a
= 1/2 ⋅ (9a + 8) ⋅ 4a
= 1/2 ⋅ 4a ⋅ (9a + 8)
= 2a ⋅ (9a + 8)
= 18a² + 16a

10.
a.
oppervlakte rood = ab
oppervlakte geel = 2a
oppervlakte blauw = 3b
oppervlakte groen = 6
oppervlakte PQRS = ab + 2a + 3b + 6
b. Ja, ze heeft gelijk.

11.
a. ab + 9a + 7b + 63
b. 6x² + 18x + 21x + 63 = 6x² + 39x + 63
c. q² - 5q + 4q - 20 = q² - q - 20
d. 6pq + 15p + 8q + 20
e. b² + 3b + 6b + 18 = b² + 9b + 18
f. 8pq + 20p - 10q - 25
g. p² + 8p + 8p + 64 = p² + 16p + 64
h. 6x² - x + 36x - 6 = 6x² + 35x - 6
i. x² - 9x - x + 9 = x² - 10x + 9

12.
(3b + 2)(a - 5) = 3ab - 15b + 2a - 10
(3b + 2)(3x - 2y) = 9bx - 6by + 6x - 4y
(3b + 2)(2b - 1) = 6b² - 3b + 4b - 2 = 6b² + b - 2
(3b + 2)(2a + b) = 6ab + 3b² + 4a + 2b

(a - 4)(a - 5) = a² - 5a - 4a + 20 = a² - 9a + 20
(a - 4)(3x - 2y) = 3ax - 2ay - 12x + 8y
(a - 4)(2b - 1) = 2ab - a - 8b + 4
(a - 4)(2a + b) = 2a² + ab - 8a - 4b

(2x + y)(a - 5) = 2ax - 10x + ay - 5y
(2x + y)(3x - 2y) = 6x² - 4xy + 3xy - 2y² = 6x² - xy - 2y²
(2x + y)(2b - 1) = 4bx - 2x + 2by - y
(2x + y)(2a + b) = 4ax + 2bx + 2ay + by

13.
a. (a + 1)(a + 1) = a² + a + a + 1 = a² + 2a + 1
b. (x - 3)(x - 3) = x² - 3x - 3x + 9 = x² - 6x + 9
c. (b - 5)(b - 5) = b² - 5b - 5b + 25 = b² - 10b + 25
d. (a - 1)(a - 1) = a² - a - a + 1 = a² - 2a + 1
e. (p + 6)(p + 6) = p² + 6p + 6p + 36 = p² + 12p + 36
f. (y + 8)(y + 8) = y² + 8y + 8y + 64 = y² + 16y + 64

14.
a. (a - 4)(a - 4) = a² - 4a - 4a + 16 = a² - 8a + 16
b. (b - 4)(b + 4) = b² + 4b - 4b - 16 = b² - 16
c. a⁴ + 2a² - 3a² - 6 = a⁴ - a² - 6
d. 3a - 9a² + 1 - 3a = -9a² + 1
e. (5a + 3)(5a + 3) = 25a² + 15a + 15a + 9 = 25a² + 30a + 9
f. (6a - 1)(6a - 1) = 36a² - 6a - 6a + 1 = 36a² - 12a + 1

15.
a. (a - 3)(a - 3) = a² - 3a - 3a + 9 = a² - 6a + 9
b. (2x + 3)(2x + 3) = 4x² + 6x + 6x + 9 = 4x² + 12x + 9

16.
a. (a + b)(a + b) = a² + ab + ab + b² = a² + 2ab + b²
b. (a + b)(a - b) = a² - ab + ab - b² = a² - b²
c. 4a² + 2a - 2a - 1 = 4a² - 1
d. 2a² + 4a - a - 2 = 2a² + 3a - 2
e. (a + 3b)(a + 3b) = a² + 3ab + 3ab + 9b² = a² + 6ab + 9b²
f. 6a² + 9ab - 2ab - 3b² = 6a² + 7ab - 3b²

17.
a.
oppervlakte parallellogram = basis x hoogte
= (2a + 4)(a - 3)
= 2a² - 6a + 4a - 12
= 2a² - 2a - 12
b.
oppervlakte trapezium = 1/2 ⋅ (a + b) ⋅ h
= 1/2 ⋅ ( (3x-1) + (4x+7) ) ⋅ (2x + 4)
= 1/2 ⋅ (7x + 6) ⋅ (2x + 4)
= 1/2 ⋅ (14x² + 28x + 12x + 24)
= 1/2 ⋅ (14x² + 40x + 24)
= 7x² + 20x + 12
c.
oppervlakte vlieger = 1/2 x korte diagonaal x lange diagonaal
= 1/2 ⋅ (2a + 6) ⋅ (3a + 5)
= 1/2 ⋅ (6a² + 10a + 18a + 30)
= 1/2 ⋅ (6a² + 28a + 30)
= 3a² + 14a + 15

18.
a.
= -6x - 15 + [ 3x² - 6x - x + 2 ]
= -6x - 15 + 3x² - 6x - x + 2
= 3x² - 13x - 13
b.
= ab - 5a - 5b² + 25b - 8b + 4a
= -5b² + ab - a + 17b
= ab - a - 5b² + 17b
c.
= 4x² + 12x + 9 - [ -4x² + x + 4x - 1 ]
= 4x² + 12x + 9 - [ -4x² + 5x - 1 ]
= 4x² + 12x + 9 + 4x² - 5x + 1
= 8x² + 7x + 10
d.
= 8x + 6x - 18 - 7x = 7x - 18
e.
= (5x - 6)(5x - 6) - [ (x + 8)(x + 8) ]
= 25x² - 30x - 30x + 36 - [ x² + 8x + 8x + 64 ]
= 25x² - 60x + 36 - [ x² + 16x + 64 ]
= 25x² - 60x + 36 - x² - 16x - 64
= 24x² - 76x - 28
f.
= (-3a + 2b)(-3a + 2b) - 5ab + 30b²
= 9a² - 6ab - 6ab + 4b² - 5ab + 30b²
= 9a² - 17ab + 34b²

19.
a.
Kies 10, 11, 12 en 13
(10 x 13) - (11 x 12)
= 130 - 132
= -2
b.
Kies 67, 68, 69 en 70
(67 x 70) - (68 x 69)
= 4690 - 4692
= -2
c.
Het verschil tussen de producten is steeds 2 (of -2).
d.
x(x + 3) - (x + 1)(x + 2)
= x² + 3x - [ x² + 2x + x + 2 ]
= x² + 3x - x² - 3x - 2
= -2