Question

31)N=(x•x²•x³•...•x la puterea 2014):(x•x²•x³•...•x la puterea 2013)
32)3x+3y=3(x+y);-2x-2y;S=(x+y)-(2x+2y)+(3x+3y)-(4x+3y)-(4x+4y)+...+(49x+49y)-(50x+50y)
33)S=(x-y+2z)+(2x-2y+4z)+...+(10x-10y+20z)
Formula de calcul prescurtat (e alte exercitii la asta)
1)(a+b)²=a²+2ab+b²;(a+b)(a-b);(a+b+c)²;(a+b)³=a³+3a²b+3ab²+b³;(a-b)²;(a-b)³
2)(x+1)²;(y+3)²;(2x+1)²;(x+2y)²;(x-2)²;(a-1)²;(3-b)²;(2a-b)²
3)(x+1)(x-1);(a-3)(a+3);(2x-1)(2x+1);(2y-3x)(2y+3x);(2x-3)²;(3x+5y)²;(11x+3)²;(3x+4y)(3x-4y)

Daca imi dati la toate exercitiile raspunsurile primiti mai multe pucte la urmatoarele probleme (promit)

Answer 1

31) N=(x•x²•x³•...•x^2014):(x•x²•x³•...•x^2013)
x•x²•x³•...•x^2013=a
obținem-> a•x^2014/a=x^2014

32) -2x-2y=-2(x+y)
S=(x+y)-(2x+2y)+(3x+3y)-(4x+4y)+...+(49x+49y)-(50x+50y)=(x+y)(1-2+3...-50)=-25(x+y)=-25x-25y
1-2+3-4...+49-50=1+(-52+52-52...+52-26)= =1+(0-26)=-25

33) S=(x-y+2z)+(2x-2y+4z)+...+(10x-10y+20z)=
(x-y+2z)(1+2+3+..9+10)=11•5(x-y+2z)=
55(x-y+2z)=55x-55y+110z

2) (x+1)^2=x^2+2x+1
(y+3)^2=y^2+6y+9
(2x+1)^2=4x^2+4x+1
(x+2y)=x^2+4xy+4y^2
(x-2)^2=x^2-4x+4
(a-1)^2=a^2-2a+1
(3-b)^2=9-6b+b^2
(2a-b)^2=4a-4ab+b^2

3) (x+1)(x-1)=x^2-1
(a-3)(a+3)=a^2-3^2=a^2-9
(2x-1)(2x+1)=(2x)^2-1^2=4x^2-1
(2y-3x)(2y+3x)=(2y)^2-(3x)^2=4y^2-9x^2
(2x-3)²=(2x)^2-2•2y•3+3^2=4x^2-12x+9
(3x+5y)²=(3x)^2+2•3x•5y+(5y)^2=9x^2+30xy+25y
(11x+3)²=121x^2+66x+9
(3x+4y)(3x-4y)=9x^2-16y^2

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