1

a

$a + 3 b + 2 a + 2 b = 3 a + 5 b$

b

$3 \cdot 40 + 5 b = 470$ $5 b = 350$ en dus $b = 70$

2

$4 a + a + 10 a = 15 a$	$a + 3 b + 4 (a + b) = 5 a + 7 b$
$3 a + 2 b + 7 a + 8 b = 10 a + 10 b$	$2 a + 4 b + 5 (a + 3 b) = 7 a + 19 b$
$4 a + 3 b + 2 a + 5 b + a = 7 a + 8 b$	$a + 2 b + 3 (5 b + 4 a) = 13 a + 17 b$

3

$5 a \cdot 7 b = 35 a b$	$3 a \cdot 4 b + 6 a b = 18 a b$
$a \cdot 5 b = 5 a b$	$2 a \cdot 3 b + a \cdot b = 7 a b$

4

a

$a$	$b$	$2 a$	$6 b$	$2 a \cdot 6 b$	$3 a$	$4 b$	$3 a \cdot 4 b$
5	2	10	12	120	15	8	120
3	4	6	24	144	9	16	144
10	3	20	18	360	30	12	360
8	2	16	12	192	24	8	192
1	5	2	30	60	3	20	60

b

De vijfde en de achtste kolom zijn gelijk, want $2 a \cdot 6 b = 12 a b$ en $3 a \cdot 4 b = 12 a b$ dus $2 a \cdot 6 b = 3 a \cdot 4 b$

5

De gelijkheid is niet juist. Neem bijvoorbeeld $a = 2$ en $b = 10$ , dan $3 a + 2 b = 3 \cdot 2 + 2 \cdot 10 = 26$ en $5 a b = 5 \cdot 2 \cdot 10 = 100$ .

6

a

$4 a$ ; $5 a$ ; $9 a$

b

4; 5; $4 \cdot 5 = 20$ routes

7

a

b

Zie opgave a.

c

8

onjuist; juist
onjuist; juist
onjuist; juist

9

$3 a^{2} + 4 a^{2} = 7 a^{2}$	${(4 a)}^{2} + 3 a^{2} = 19 a^{2}$
$4 a \cdot 3 a + 3 a \cdot 3 a = 21 a^{2}$	$a \cdot 2 a + 5 a \cdot a = 7 a^{2}$
$4 \cdot (a \cdot 4 a) = 16 a^{2}$	$3 \cdot {(5 a)}^{2} = 75 a^{2}$

10

$a \cdot (4 a + b) = a \cdot 4 a + a \cdot b = 4 a^{2} + a b$
$3 a \cdot (3 a + 2 b) = 3 a \cdot 3 a + 3 a \cdot 2 b = 9 a^{2} + 6 a b$
$2 a \cdot (4 a + b) = 2 a \cdot 4 a + 2 a \cdot b = 8 a^{2} + 2 a b$

11

$5 a^{2} + 20 a b = 5 a \cdot (a + 4 b)$
$a^{2} + 8 a b = a \cdot (a + 8 b)$
$3 a^{2} + 9 a b = 3 a \cdot (a + 3 b)$

12

a

$lengte \times breedte: (2 a + 2 b) \cdot (3 a + b)$
$6 a^{2} + 8 a b + 2 b^{2}$

b

$(2 a + 2 b) \cdot (3 a + b) = 6 a^{2} + 8 a b + 2 b^{2}$

c

$(2 \cdot 60 + 2 \cdot 90) \cdot (3 \cdot 60 + 90) = 300 \cdot 270 = 81000$

13

a

De oppervlakte is $l b$ .
De omtrek is $2 l + 2 b = 2 (l + b)$ .

b

De oppervlakte is $2 l \cdot 2 b = 4 l b$ .
De omtrek is $4 l + 4 b = 4 (l + b)$ .

14

a

$(a + b) \cdot (c + d) = a c + a d + b c + b d$

b

$(a + 2 b) \cdot (3 c + 4 d) = 3 a c + 4 a d + 6 b c + 8 b d$

c

${(a + b + c)}^{2} = (a + b + c) \cdot (a + b + c) = a^{2} + b^{2} + c^{2} + 2 a b + 2 a c + 2 b c$

d

${(a + 2 b + 3 c)}^{2} = (a + 2 b + 3 c) \cdot (a + 2 b + 3 c) = a^{2} + 4 b^{2} + 9 c^{2} + 4 a b + 6 a c + 12 b c$

15

a

8

b

$b^{3}$ ; $a^{2} b$ ; $a b^{2}$

c

${(a + b)}^{3} = (a + b) \cdot (a + b) \cdot (a + b) = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$

d

${(3 + 2)}^{3} = 5^{3} = 5 \cdot 5 \cdot 5 = 125$ en $3^{3} + 3 \cdot 3^{2} \cdot 2 + 3 \cdot 3 \cdot 2^{2} + 2^{3} = 27 + 54 + 36 + 8 = 125$ . Dit klopt.

e

$11^{3} = {(10 + 1)}^{3} = 10^{3} + 3 \cdot 10^{2} \cdot 1 + 3 \cdot 10 \cdot 1^{2} + 1^{3} = 1000 + 300 + 30 + 1 = 1331$

f

${(2 a + b)}^{3} = {(2 a)}^{3} + 3 \cdot {(2 a)}^{2} \cdot b + 3 \cdot 2 a \cdot b^{2} + b^{3} = 8 a^{3} + 12 a^{2} b + 6 a b^{2} + b^{3}$

16

a

$6 a + 8 c$

b

$14 a$