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EXEMPLES – MODEL

T.1 Signes i parèntesis

2 – 3·(7 – a) = 2 – 3·7 + 3·a = 2 – 21 + 3·a = –19 + 3·a

T. 2 Factorització (Treure factor comú i Suma per diferència)

A) 3xy + 12x2y3 = 3xy·(1 + 4xy2)


B) 9x2 – 121y4 = (3x + 11y2)(3x – 11y2)

T. 3 Suma de fraccions

7 – 27 + 7 –20
– 3 + ( = (((( = ((
9 99

3 1 3·15 – 1·4 41
(( – (( = ((((( = ((
20 75 300 300

20 = 22·5 ( 3·5 = 15
75 = 3·52 ( 22 = 4
mcm = 22·3·52 = 300

9 – 2x 14 – 9 + 2x 5 + 2x
2 – (((( = ((((( = ((((
7 7 7

T. 4Producte de fraccions

13 28 13·28 4
( · (( = ((( = (
7 39 7· 39 3

T. 5 Quocient de fraccions

3 3 9 27
( (( = 3· ( = ((
7 3 1 17 7 7
(( = ( · ( = (( (
9 7 9 21 9
T. 6 Propietats de les potències

(82·85)3 = (87)3 = 87·3 = 821

23 –5 1
(( = 23 – 5+2 = 23 –3 = ((
23 –2 233

T. 7 Jerarquia de les operacions

5 + 2·92 = 5 + 2·81 = 5+ 162 = 167

(2 –1 – 3·4–1) – 1 = (1/2 – 3/4)– 1 = (–1/4) – 1 = – 4/1 = – 4

T. 8 Quadrat d’un binomi

(5x2 – 9y3)2 = 25x4 + 81y6 – 90x2y3

T. 9 Propietats de les arrels

[pic] = [pic] [pic]

T.10 Extracció i introducció de factors dins un radical

[pic] = [pic] = [pic] = [pic]

T.11 Racionalització

A) [pic] [pic][pic]3 3 ([pic]+ 3 ) 3 ([pic]+ 3 )
B) (((( = (((((( = (((((
[pic] – 3 7 – 32 – 2

T.12 Exponents fraccionaris

[pic] = [pic] = [pic] = [pic] = [pic] = [pic]

Exercicis T.1 (/ T.7)
|1 – 2·(3 – 3·5) = |5 – 7·(3·2 – 4) =|
|3 – 5·(1 – 4·5) = |9 – 8·(4·3 – 5) = |
|–10 + 2·(1 – 3·5) = |–5 – 7·(3·4 – 8) = |
|– 14 + 3·(4 – 2·5) = |–8 – 7·(2·5 – 6) =|
|a – 2·(a – 3) = |5a – 7·(2 – a) = |
|2a – 4·(3a – 2·5) = |7a – 8·(3 – 2a) = |
|3a – 5·(4a – 4·3) = |9a – 8·(7 – 5a) =|
|3 – 5·(4a + 4·3) = |9a – 5·(7 + 5a) = |
|12 – 2·(3a + 4·5) = |17a – 6·(4 + 2a) = |
|32 – 6·(2a + 2·5) = |–3a – 4·(3 + 2a) =|

Exercicis T. 2A
|4x + 8xy = |5xy – 5y = |
| | |
|3x + 9x2y = |6x2y – 3x =...