Question

4)(x+3y)²+(x-3y)(x+3y);(4x-3)²+5x(-3);(1+x)²+(3+x)²;(x²+y)²-(x²y)²
5)(x+4)²-(x-2)²-2x²;(2x-3)²-(3x+5)²+(2x+5)²+(2x-5);(x+5)²-(x-2)(x+2)+2(x+1)²;(3+4x)²+4(x-2)²-(x+3)(x-3)
6)(2+√5)²;(√5+√6)²;(√6-√2)²;(5-√3)(√5+√3);(√6-2)(√6+2)
7)(√12+1)²;(√3+√2)²;(√8-3)²;(√£10-√6)²;(√13-√5)(√13+√5);(5-√6)(5+√6)
8)(√3-1)²+√12;(√5-√3)²+2√5•√27;2(√7+1)²-2(√7-2)²;(√8+√3)²+(√6-1)(√6+1)
9)33²;51²;43²;103²:calculati rapid,folosind formulele de calcul prescurtat
10)calculati rapid,folosind formulele de calcul prescurtat:69²;27²;87²;98²
11)calculati rapid,folosind formulele de calcul prescurtat:28•32;35•45;57•63;96•106
12)(2√3+x)²;(3√3x+2√5)²;(1\2x+3)²;(3-2√3)²;(3-2√3)²;(2√5x-3√2x)²;(5√2x-4√3y)²
13)(8x-4√5)(8x+4√5);(7√2a-5√6b)(7√2a+5√6b);(√2x-3y)(2√x+3y);(1\3x-3\2)²;(√2\2x+1\√2y)²;(1\3x-5\6yz)(1\3x+5\6yz)
15)(7√3+√2)²-2(1+7√6);2√5(√3-1)+(√5-√3)²;12√75+(6-5√3)²;(3√7-2√6)²+60√126:(5√3)

Answer 1

4)(x+3y)²+(x-3y)(x+3y)=x²+6y+9y²+x²-9y²=2x²+6y

(4x-3)²+5x•(-3)=16x²-24x+9-15x=16x²-39x+9

(1+x)²+(3+x)²=1+2x+x²+9+6x+x²=2x²+8x+10

(x²+y)²-(x²y)²=x⁴+2x²y+y²-x⁴y²

5)(x+4)²-(x-2)²-2x²=x²+8x+16-x²+4x-4=12x+12

(2x-3)²-(3x+5)²+(2x+5)²+(2x-5)=4x²-12x+9-9x²-30x-25+4x²+20x+25+2x-5=-x²-20x+4

(x+5)²-(x-2)(x+2)+2(x+1)²=x²+10x+25-x²+4+2x²+4x+2=2x²+14x+29

(3+4x)²+4(x-2)²-(x-3)(x+3)=9+24x+16x²+4(x²-4x+4)-x²+9=15x²+24x+9+4x²-16x+16+9=19x²+8x+34

6)(2+√5)²=2+4√5+5=7+4√5

(√5+√6)²=5+2√30+6=11+2√30

(√6-√2)²=6-2•2√3+2=8-4√3

(5-√3)(5+√3)=25-3=22

(√6-2)(√6+2)=6-4=2

7)(√12+1)²=12+2√12+1=13+2√12

(√3+√2)²=3+2√6+2=5+2√6

(√8-3)²=8-6•2√2+9=17-12√2


(√10-√6)²=10-2√60+6=16-4√15


(√13+√5)(√13-√5)=13-5=8

(5-√6)(5+√6)=25-6=19

8)(√3-1)²+√12=3-2√2+1+2√3=4+2(√3-√2)

(√5-√3)²+2√5•√27=5-2√15+3+6•√5•√3=
8+4√15

2(√7+1)²-2(√7-2)²=2((√7+1)²-(√7-2)²)=2(7+2√7+1-7+4√7+4)=2(6√7+5)=12√7+10

(√8+√3)²+(√6-1)(√6+1)=8+2√24+9+6-1=22+4√6

9)33²=1089

51²=2754

43²=1849

103²=10 609

10) 69²=4554

27²=729

87²=7569

98²=9604

11) 28•32=896

35•45=5²•7•9=25•63=1575

57•63=3591

96•106=10176

12)(2√3+x)²=12+4√3•x+x²

(3√3x+2√5)²=27x²+2•6√15+20=27x²+12√15+20

(1/2x+3)²=1/4•x²+3x+9

E suficient pentru 8 puncte