Question

1 . Descompuneti in factori:
a) 8 x^2 -16x+12
b) 3(x-1)+x(x-1)
c) (2x+3)(x+3)-(2x+3)(2x-1)
d) 2ax-6y+3ay-4x

3. Factorizati expresiile :.
a) 25x^2-40x+16
b) 100x^2 -16
c) 4x^2 -(x+2)^2
d) x^2-y^2+2yz-z^2
4. Daca (x+y)^2 = 12 xy=3 , atunci x^2+y^2 va fi.....( vreau rezolvare completa ... nu doar raspuns)
5. Descompuneti in factori:
a) 10a+15a^2-5
b) a(2-3)+3a-3
c) (a+3)(2a-1)+(2a-1) (a+2)
d) a^3 + a^2 -4a-4
6. Factorizati expresiile:
a) -4a+4+a^2
b) 81-25 a^2
c) (a-3)^2 -16 a^2
7. Desc. in factori:
a) a^2 +16a +48
b ) a^2 -2a -15
8. Daca. a+ 1/a = 3 , atunci a^2 +1/a^2 =..........( rezvare completa)
La toate exercitiile rezolvare completa nu direct la raspuns va rog ca sa inteleg!!!

Answer 1

1 . Descompuneti in factori:
a) 8 x² -16x+12=4(x²-2x+3)  
b) 3(x-1)+x(x-1)=(x-1)(3+x)
c) (2x+3)(x+3)-(2x+3)(2x-1)=(2x+3)(x+3-2x-1)=(2x+3)(2-x)
d) 2ax-6y+3ay-4x=2ax-4x-6y+3ay=2x(a-2)+3y(a-2)=(a-2)(2x+3)

3. Factorizati expresiile :.
a) 25x²-40x+16=(5x-4)²
b) 100x² -16=(10x-4)(10x+4)
c) 4x² -(x+2)²=(2x-x-2)(2x+x+2)=(x-2)(3x+2)
d) x²-y²+2yz-z² =x²-(y²-2yz+z²)=x²-(y-z)²=x-y+z)(x+y-z)
4. Daca (x+y)² = 12 xy=3 , atunci x²+y² va fi.....
(x+y)² = 12
x²+2xy+y²=12    inlocuim xy=3
x²+2×3+y²=12
x²+y²=12-6
x²+y²=6
5. Descompuneti in factori:
a) 10a+15a²-5=10a²+10a+5a²-5=10a(a+1)+5(a²-1)=10a(a+1)+5(a-1)(a+1)=
=5(a+1)(2a+a-1)=5(a+1)(3a-1)
b) a(2-3)+3a-3=-a+3a-3=2a-3
c) (a+3)(2a-1)+(2a-1) (a+2) 
d) a³ + a² - 4a - 4 =a²(a+1)-4(a+1)=(a+1)(a²-4)=(a+1)(a-2)(a+2)
6. Factorizati expresiile:
a) -4a+4+a² =a²-4a+4=(a-2)²
b) 81-25 a² =(9-5a)(9+5a)
c) (a-3)² -16 a²=(a-3-4a)(a-3+4a)=(-3a-3)(5a-3)=-3(a-1)(5a-3)
7. Desc. in factori:
a) a² +16a +48=a²+12a+4a+48=a(a+12)+4(a+12)=(a+12)(a+4)
b ) a² -2a -15 =a²+3a-5a-15=a(a+3)-5(a+3)=(a+3)(a-5)
8. Daca. a+ 1/a = 3 , atunci a² +1/a² =.......... 
 a+ 1/a = 3  ridicam la puterea 2
a²+1/a²+2a×1/a=9
a²+1/a²+2=9
a²+1/a²=7