Page 49 - matematica-viii
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Capitolul 2
47
UNIT A TEA 2 Calcul algebric în ℝ 47
Recapitulare
1. Calculați: 6. Calculați, folosind formulele de calcul prescurtat:
a) 4 x + 5x–8 + x –1–7x ; a) (4x − 1) − (3x + 1) (3x − 1) − ( x − 2x) ;
2
2
2
2
2
_
_
_
_
_
7)
6
2
6
b) 7 x –2x–5–3 x + 6x + 8 ; b) (2 √ x − √ − ( √ x − 2) ( √ x + 2) − 2x (x − 2 √ 14 ) ;
2
2
2
2 2 2
2 _
4 _
3 _
4 _
2 _
1 _
c) x –4x + 7–2 x + 5x–3 x –4 + 6 x ; c) x + x + ( x − ) − x − x ;
3
2
3
2
2
2
2
5 )
2
5 )
(5
(5
_
_
_
_
_
3 _
7 _
d) a + 2ay − ay + 4a ; d) ( √ x + 3) − (2 √ x − √ (2 √ x + √
5
5
3) ⋅
3) +
5
2
5
2
_
e) 13, 4 x –5, 24 + 3, 61x + 4, 15–6, 71 x + 4, 9x ; + (3 √ x − 1) ;
2
2
5
2
0, 3
0, 5
_
3 _
_
f) x − x + x + x + 5 ; e) [ (6x − 1) (3x + 2) − (2x − 5) (9x + 1) ] [ (x − 4) (x + 3) −
2
2
2
2
4
7 _
3 _
7 _
1 _
5 _
3 _
g) x + x − x + − x + ; − (x + 4) (x − 5) ] .
2
2
2
2
5
2
4
3
h) 3, (1) x –5, 2x + 4, 3 (2) + 6, (3) x–5, 6 x + 7, 1 . 7. Descompuneți expresiile în factori:
2
2
2. Calculați: a) 7x (1–2x) –5 (1–2x) ;
a) 2x + 3x − 2 + 4x − (5x + 4 ) + (3x + 2) ; b) 32 x –8 x + 16 x –4 x ;
5
4
2
3
4
4
b) ab + 2 − (3ab − 5 ) + (4ab + 1 ) − ab − 2 ; c) 6 a b c –9 a b c + 12 a b c ;
2
3
3
3
5
2
4
c) 3 (4x–6) –4x (x + 3) ; d) (3–2x) (x–3) – (x–3) (1–4x) ;
d) 4x · (x–5) –3 · ( x + 3x–1) + 2 · (2x –1) ; e) (x–3) (2x–5) – (3–x) (4–3x) ;
2
e) (16 x –5 x + 3x) : (0, 5x) ; f) 12 x –8 x –15x + 10 ;
3
2
2
3
f) (6 a x y –12 a x y –9 a x y ) : (– 3 a x y ) ; g) (2x–3) –4x (2x–3) –5 (2x–3) ;
2
3
2
3
2
4
2
3
3
2
2
2
3
3
g) (3 a x –5 a x + 6 a x ) : (2 a x ) ; h) (2 − x) + 2x (2 − x) − 5 (x–2) .
4
2
3
2
3
4
2
4
4
3
h) 7 x (x–2) –5x (3 x –6x–4) + 4 (2 x –4 x –5x + 3) . 8. Descompuneți expresiile în factori:
2
2
2
3
_
3. Calculați: a) 16–40x + 25 x ; b) 3 x − 2 √ x + 1 ;
3
2
2
a) (2 x –3x–1) (x–1) ; c) 81–4 x ; d) 16 x –3 ;
2
2
2
_ _ _ _ _ _ _
b) 2 √ ⋅ ( √ − 2x) + √ ⋅ (2 √ x + 3 √ 2 6 ) e) (4x–3) –25 ; f) 25 x – (2x–1) ;
3
2
6
2
3) − √ ⋅ (8 − x √ ;
2
3
2
c) ( x + x + x ) (x–1) ; g) (6x–1) – (4x–3) ; h) (7x–4) – (2x–3) ;
2
2
2
3
2
2
4
_
d) [–5x · (8 x –4 x ) –10x · (6 x –4x) ] : (–20 x ) ; i) 9 x − 6 √ x + 2 .
2
4
2
4
2
3
2
e) ( x –x + 1) ( x + x + 1) ; 9. Descompuneți expresiile în factori:
2
2
f) [ (3 x –2x–4) · (x–2) – ( x + 4x–8) · (x + 1) ] : (8x) ; a) x − x y + x y − y ; b) x + 2 x − 3x − 6 ;
2
2
3
2
3
3
2
2
g) [2x + 1– (x + 2) ] [3x–2– (2x–3) ] ; c) x − 10x + 16 ; d) x − 6x − 16 ;
2
2
_ _ _ _ _
h) 3 √ 3 3(2x + 3 √ 7 e) 9 x − 6x − 15 ; f) 16 x − 8x − 24 ;
7) + 3 √ x (2x + 1) −
7(2 √ − x) − 2 √
2
2
_
– 6 x √ . g) x − 3x − 28 ; h) 6 x –3 x –10x + 5 ;
7
2
3
2
2
4. Calculați aria unui pătrat care are perimetrul egal cu i) 4 x − 8 x − 140x .
2
3
4ab metri, a, b ∈ ℕ . 10. Descompuneți expresiile în factori:
5. Calculați, folosind formulele de calcul prescurtat: a) ( x + x + 1) ( x + x + 3) + 1 ;
2
2
a) (2x–3) ; b) (4x–3) (4x + 3) ; c) (4x − 3) ; b) ( x –x + 2) ( x –x + 4) + 1 ;
2
2
2
2
_
_
3
d) [0, (2 ) + 3x] ; e) ( √ x + √ ; c) ( x –x) ( x –x + 5) − 6 ;
5)
2
2
2
2
f) (2x − 5) (2x + 5) ; g) (0, 3x − 7, 3) (0, 3x + 7, 3) ; d) ( x − x + 1) + 2 ⋅ ( x − x + 1) − 3 .
2
2
2
_
_
3 _
7 _
3 _
7 _
5)
h) x − x + ; i) ( √ x + √ − 10 . Indicație. Folosiți substituții/notații convenabile.
3
2
6 )
(4
6 )(4
