Question

Deschideti parantezele si reduceti termeni asemenea:
a) 5(x-1)+2x+3
b) 3(1-x)+2-3x
c) 3x(x-1)-17+x(1+3x)+1
d) 2(x+1)-1+3*(1-2x)
e) (x+5)(x+3)+(x-1)(x+7)+10
f) 2x-(x+2)(x-2)+5-(x-1)
g) (x+1)(x-3)(x+5)(x+7)
h) (x-4)(x-5)(x-6)(x-7)

Answer 1

a) 5(x-1)+2x+3=5x-5+2x+3=7x-2

b) 3(1-x)+2-3x=3-3x+2-3x= - 6x+5

c) 3x(x-1)-17+x(1+3x)+1=3x²-3x-17+x+3x²+1=6x²-2x-16

d) 2(x+1)-1+3*(1-2x)=2x+2-1+3-6x=-4x+4=4(1-x)

e) (x+5)(x+3)+(x-1)(x+7)+10=x²+3x+5x+15+x²+7x-x-7+10=2x²-14x+3

f) 2x-(x+2)(x-2)+5-(x-1)=2x-(x²-2x-2x+4)+5-x+1=-x²+2x+2

g) (x+1)(x-3)(x+5)(x+7)=(x²-3x+x-3)(x²+7x+5x+35)=(x²-2x-3)(x²+12x+35)=
=x^4-10x^3-32x^2-130x-105

h) (x-4)(x-5)(x-6)(x-7) =(x²-5x-4x+20)(x²-7x-5x+42)=(x²-9x+20)(x²-12x+42)=
=x^4-21x^3-170x^2-+840

Answer 2

a)5(x-1)+2x+3=5x-5+2x+3=7x-2=0⇒7x=2⇒x=2/7
b)3(1-x)+2-3x⇒3-3x+2-3x=0⇒-6x+5=0⇒-6x=-5⇒x=-5/6
c)3x(x-1)-17+x(1-3x)+1=3x²-3x-17+x-3x²+1=-2x-16=0⇒-2x=16⇒x=16/-2⇒x=-8
d)2(x+1)-1+3(1-2x)=2x+2-1+3-6x⇒-4x-4=0⇒-4x=4⇒x=-4/4⇒x=-1
e)(x+5)(x+3)+(x-1)((x+7)+10=x²+3x+5x+15+x²+7x-x-7+10=
2x²+14x+18

f)2x-(x+2)(x-2)+5-(x-1)=
2x-(x²-2x+2x-4)+5-x+1=2x-x²+4+5-x+1⇒-x²+x+10

g)(x+1)(x-3)(x+5)(x+7)=
(x²-3x+x-3)(x²+7x+5x+35)⇒(x²-2x-3)(x²+12x+35)=x⁴+12x²+35x-2x³-48x²-70-3x²--36x-105=
x⁴+9x³+8x²-36x

h)(x-4)(x-5)(x-6)(x-7)=..
(x²-5x-4x+20)(x²-7x-6x+42)=
(x²-9x+20)(x²-13x+42)=x⁴-13x³+42x²-9x³+117x²-378x+20x²-260+840
x⁴-22x³+137x²-378x+580
succes
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