Question

30.Efectuati urmatoarele calcule si reduceti termenii asemenea:
a) 2x(3-2x)+(-x)^2 ( 2x-3)+(-x)(x^2-2x+1)=
b) (18x^3+9x^2-3x): (-3x)+ (24x^4-36x^5+72x^3):(12x^3)=
c) ( 18x^60-36x^40+99x^70):(-9x^30)=
d) ( 12x^n+1+ 30x^n+2- 42x^n): (6x^n)=

31. Aratati ca N este patrat perfect, oricare ar fi numarul natural nenul x:
N=(x•x^2•x^3•....•x^2014) : (x•x^2•x^3•...•x^2012)

Answer 1

$30a).2x(3-2x)+(-x)^2(2x-3)+(-x)(x^2-2x+1)= \\ =6x-4x^2+x^2(2x-3)-x^2+2x^2-x= \\ =6x-4x^2+2x^3-3x^2-x^2+2x^2-x=2x^3-5x^2+5x \\ b).(18x^3+9x^2-3x):(-3x)+(24x^4-36x^5+72x^3):(12x^3)= \\ =-6x^2-3x+1+2x-3x^2+6=-9x^2-x+7 \\ c).(18x^{60}-36x^{40}+99x^{70}):(-9x^{30})= -2^{30}+4x^{10}+11x^{40}= \\ =-x^{10}(2x^{20}-4+11x^{30})$
$d).(12x^{n+1}+30x^{n+2}-42x^n):(6x^n)= 2x+5x^2-7=5x^2+2x-7$
$31).N=(x \cdot x^2 \cdot x^3 \cdot ... \cdot x^{2014}):(x \cdot x^2 \cdot x^3 \cdot ... \cdot x^{2012}) \\ N=x^2-p.p$