Question

a) (2x +4)(x-1)+(3x-5)(x-2)
b) (5x-3y)(2Y-7)-(5x+3y)(7-2y)
c) (0,1 a- 0,5)(10a+2)-(0,2a+0,1) (10a-4)
d) (√3x-√7)(√7x-3)-(√3x-3)(√7x-1)
2)Efectuati respectand ordinea operatiilor:
a) (6x+3):3+(12x-16):4
b) ( 3 a la puterea 2 -6a):(3a) - (16 a la put 4 -24 a la a 3 ) : (8a la put 3 ) =(x-2) √3 +√2(y+7)=0
c) (8x la a 3 + 6x la put 2 +4x):(-1 pe2 x) +( 3 pe 4 x la put 2 - 1 pe 2 x -0,25) ori 4x
d) [(12 a la put 3 - 4 a la put 2 ):(2a) -6a la put 2 +2a]:(-2a)
e) [( 5x +7)(5x-7)+49]:(-25) - x la put 2
f) (x-√2)(x+√2)+(x+√3)(√3-x) -(2√3x -4√3 ):(2√3)
g{[(2 a -3)(2a+3)-a la put 2 ] :(-3) +a (3-2a)}:(-3)
3) Calculati:
a) (x+1)(x la put 2-x+1)
b) (x-2) ( x la put 2 +2x+4)
c) (x la 2 -2x)(x la 2,+3x -5)
d) 2x (x+3)(x-2)
e) 5a (2a-5)(3a+4)
f) (x+1)(x+2)(x+3)
g) (3-x)(x+3) (x la put 2 +9)
h) (a-5)(a-1)(a-2)
i) ( 1pe2 a-b) ( 2 pe 3 a+b ) (a-1 pe 3 b)
j) (x+√3)(x+√2)(x-√3)
k) (√5-2√3) (√5a+2√3 )(5a la put 2 +12)
l) ( x la put 2 +x+1)(x la put 2, +2x +3)
m) (2a-b+3)(3a+2b+1)
n) ( 3 a la put 2- 2 a +4 )(a la put 2 -2a -

Answer 1

a)(2x +4)(x-1)+(3x-5)(x-2)= =2x²+4x-2x-4+3x²-5x-6x+10= =5x²-9x+6 b) (5x-3y)(2y-7)-(5x+3y)(7-2y)== (5x-3y)(2y-7) + (5x+3y)(2y-7)==(2y-7)(5x-3y+5x+3y)=(2x-7)10x=20x²-70x 
c) (0,1 a- 0,5)(10a+2)-(0,2a+0,1) (10a-4) ==(a/10-1/2)(10a+2)-(a/5+1/10)(10a-4) ==(a²-5a+a/5-1)-(2a²+a-4a/5-4) ==a²-5a+a/5-1-2a²-a+4a/5+4) ==-a²-5a+3

2)Efectuati respectand ordinea operatiilor:
a) (6x+3):3+(12x-16):4== 2x+1+3x-4=5x-3
b) ) ( 3a² -6a):(3a) - (16a⁴ -24a³) : (8a³) =
= a -2 - 2a +3 =1-a

c) (8x³+ 6x² +4x):(-1/2 x) +( 3/4x² – 1/2 x -0,25) * 4x== (8x³+ 6x² +4x)*(-2/x) +( 3x²/4 – x/2 -0,25) * 4x== -16x²-12x -8 + 3x³ – 2x² -x== 3x³-18x²-13x -8  
d) [(12 a³ - 4 a² ):(2a) -6a² +2a]:(-2a) == (6 a² - 2 a  -6a² +2a):(-2a) =0 e) [( 5x +7)(5x-7)+49]:(-25) - x²== ( 25x² -49+49):(-25) - x²== ( 25x² ):(-25) - x²== -x² - x²=-2 x² f) (x-√2)(x+√2)+(x+√3)(√3-x) -(2√3x -4√3 ):(2√3)== x²-2+3-x² -x +2=3-x g{[(2 a -3)(2a+3)-a²] :(-3) +a (3-2a)}:(-3)== {[(4a² -9)-a²] :(-3) +(3a-2a²)}:(-3)== [(3a² -9) :(-3) +(3a-2a²)]:(-3)==(-a² +3 +3a-2a²):(-3)==(-3a² -3 +3a):(-3)==a² -3a +3 3) Calculati:
a) (x+1)(x²-x+1)=x³+1
b) (x-2) ( x² +2x+4)=x³-8
c) (x² -2x)(x²+3x -5)=x⁴-2x³+3x³-6x²-5x²+10x== x⁴+x³-11x²+10x  d) 2x (x+3)(x-2)== (2x²+6x)(x-2)==2x³+6x²-4x²-12x==2x³+2x²-12x==2x(x²+2x-6)

e) 5a (2a-5)(3a+4)== (10a²-25a)(3a+4)== 30a³-75a²+40a²-100a== 30a³-25a²-100a==5a(6a²-5a-20)