1

a

$5 \cdot 16 x^{2} = 80 x^{2}$ ; $5 - 16 x^{2}$ ; $25 - 40 x + 16 x^{2}$ ; $x^{2}$

b

$‐ (2 x - y - (2 x - 2 y)) = ‐ (2 x - y + (‐ 2 x + 2 y)) = ‐ y$
$(‐ 2 x + y) - (2 x - 2 y) = (‐ 2 x + y) + (‐ 2 x + 2 y) = ‐ 4 x + 3 y$
$‐ 2 x + (y + (‐ 2 x + y)) = ‐ 2 x + (‐ 2 x + 2 y) = ‐ 2 x + (‐ 2 x + 2 y) = ‐ 4 x + 2 y$
$2 x - y + 2 (x - y) = 2 x - y + 2 x - 2 y = 4 x - 3 y$

c

$4 x^{2} - 20 x - 25$
$‐ 4 x^{2} - 20 x - 25$
$2 (x^{2} - 10 x + 25) = 2 x^{2} - 20 x + 50$
${(2 x - 10)}^{2} = 4 x^{2} - 40 x + 100$

d

$3 (x y - 2 x + y - 2) = 3 x y - 6 x + 3 y - 6$
$3 x + 3 + y - 2 = 3 x + y + 1$
$3 x + 3 - y + 2 = 3 x - y + 5$
$3 + (‐ x + 1) + (‐ y + 2) = ‐ x - y + 4$

e

$(x + 4) (x + 6)$	$(x - 5) (x + 5)$
$(x - 12) (x + 2)$	$(x - 5 y) (x + 5 y)$
$(x - 2) (x + 12)$	$(x + 1) (y + 1)$
$(x - 6) (x - 4)$	$(x + 1) (y - 1)$

2

a

$\frac{1}{4}$ m²

b

${(x + 5)}^{2} - x^{2}$

c

${(x + 5)}^{2} - x^{2} = 800 \cdot \frac{1}{4}$

d

$x^{2} + 10 x + 25 - x^{2} = 200$
$10 x + 25 = 200$
$10 x = 175$
$x = 17,5$
17,5 bij 17,5 meter

3

a

gewicht kiwi $= 340 - a$
gewicht peer $= 400 - a$

b

vergelijking: $340 - a + 400 - a = 300$
oplossing: $740 - 2 a = 300$
$‐ 2 a = ‐ 440$
$a = 220$

c

De appel weegt 220 gram, de kiwi 120 gram en de peer 180 gram.

4

a

$3 \frac{3}{4}$ , $8 \frac{3}{4}$ , $15 \frac{3}{4}$ , $24 \frac{3}{4}$

b

Het is het kwadraat van het grootste getal.

c

$n^{2} - \frac{1}{4}$

d

$10^{2} - \frac{1}{4} = 99 \frac{3}{4}$

5

a

$(2 x - 3) - (‐ x + 1) = 3 x - 4$

b

$3 x - 8 \frac{1}{2} = \frac{1}{2} ((‐ x + 1) + (2 x - 3))$
$3 x - 8 \frac{1}{2} = \frac{1}{2} (x - 2)$
$3 x - 8 \frac{1}{2} = \frac{1}{2} x - 1$
$6 x - 17 = x - 2$
$5 x - 17 = ‐ 2$
$5 x = 15$
$x = 3$
controle:
Als je voor $x = 3$ neemt, dan
$‐ x + 1 = ‐ 2$ en $2 x - 3 = 3$ .
$3 x - 8 \frac{1}{2} = \frac{1}{2}$ ; en $\frac{1}{2}$ ligt midden tussen $‐ 2$ en 3.

6

a

oplossing:
$x + (‐ 1 + x) + 8 = 9 + 3 x$
$2 x + 7 = 9 + 3 x$
$‐ 2 = x$
controle:
$‐ 2 - (1 - ‐ 2) + 8 = ‐ 2 - 3 + 8 = 3$
$3 (3 + ‐ 2) = 3 \cdot 1 = 3$

b

oplossing:
$x^{2} - 9 = x^{2} - 2 x - 3$
$‐ 9 = ‐ 2 x - 3$
$‐ 6 = ‐ 2 x$
$x = 3$
controle:
$(3 + 3) (3 - 3) = 6 \cdot 0 = 0$
$(3 + 1) (3 - 3) = 4 \cdot 0 = 0$

c

oplossing:
$x + (‐ \frac{3}{2} x - 2) = ‐ 2 \frac{1}{2} + x$
$‐ \frac{1}{2} x - 2 = ‐ 2 \frac{1}{2} + x$
$‐ 1 \frac{1}{2} x = ‐ \frac{1}{2}$
$3 x = 1$
$x = \frac{1}{3}$
controle:
$\frac{1}{3} - \frac{1}{2} (1 + 4) = \frac{1}{3} - 2 \frac{1}{2} = ‐ 2 \frac{1}{6}$
$‐ (2 \frac{1}{2} - \frac{1}{3}) = ‐ 2 \frac{1}{6}$

7

a

$B F = B D = 55 - x$
$C E = C D = 30 - x$

b

$B C = 45$ en $B C = B D + C D = 55 - x + 30 - x$
Dus $45 = 85 - 2 x$
Dus $2 x = 40$ , $x = 20$

8

a

$∠ B A C = ∠ B A M + ∠ C A M = ∠ C + ∠ B = 12 + 38 = 50 °$
$∠ A M B = 180 - 2 \cdot 38 = 104 °$
$∠ A M C = 180 - 2 \cdot 12 = 156 °$
$∠ B M C = 360 - ∠ A M B - ∠ A M C = 360 - 104 - 156 = 100 °$

b

$∠ B A C = (b + c) °$
$∠ B M A = (180 - 2 b) °$
$∠ C M A = (180 - 2 c) °$
$∠ B M C = 360 - ((180 - 2 b) + (180 - 2 c)) = 360 - (360 - 2 b - 2 c) = 360 + (‐ 360 + 2 b + 2 c) = (2 b + 2 c) °$

c

$∠ B M C$ is 2 keer zo groot als $∠ B A C$ .