Question

Dam naj na jutro
zadanie 1 wykonaj potegowanie
a) (2x+1) do potegi 3
(2x-3) do potegi 3
(2x-1) do potęgi 3
b) (4x-3) do potęgi 3
(3x-4) do potęgi 3
(4x-4) do potęgi 3
zadanie 2
Wykonaj działania.

a) 2(x-2)3-(2x-1)3

b) (-3-2x)3+(2x+3)3

c) 3(x-2)3-2(2x-1)3+4x(2x-1)2

d) (3x-1)3-2(x+2)3+x(5x+1)2


e) (x2+1)3-(x3+1)2

f) [(x+1)2+(2-x)(2+x)]3

g) (x2-2x)3-(x2+2x)3

h)(2x2-3x)3+(3x-2x2)3

Answer 1

Zad1(2x+1)³=(2x)³+3(2x)²*1+3*2x*1²+1³=8x³+12x²+6x+1
(2x-3)³=(2x)³-3(2x)²*3+3*2x*3²-3³=8x³-36x²+54x-27
(2x-1)³=8x³-12x²+6x-1
b) (4x-3)³=(4x)³-3(4x)²*3+3*4x*3²-3³=64x³-144x²+108x-27
(3x-4)³=27x³=108x²+144x-64
(4x-4)³=64x³-192x²+192x-64
zad2a)
2(x-2)³-(2x-1)³=2(x³-6x²+12x-8)-(8x³-12x²+6x-1)=2x³-6x²+12x-8-x³+12x²-6x+1=x³+6x²+6x-7
b) (-3-2x)³+(2x-3)³=(-3)³-3*(-3)²*2x+3(-3)*(2x)²-(2x)³+8x³-24x²+54x-27=
=-27-54x²-36x-8x³+8x³-24x²+54x-27=-78x²+18x-54
c)3(x-2)³-2(2x-1)³+4x(2x-1)²=3(x³-6x²+12x-8)-2(8x³-12x²+6x-1)+4x(2x²-2x+1)=
=3x³-18x²+36x-24-16x³+24x²-12x+2+8x³-8x²+4x=-5x³+28x-22

d)(3x-1)³-2(x+2)³+x(5x+1)²=27x³-27x²+6x-1-2(x³+6x²+12x+8)+x(25x²+10x+1)=
=27x³-27x²+6x-1-2x³-12x²-24x-16+25x³+10x²+x=50x³-29x²-17x-17

e)(x²+1)³-(x³+1)²=x^6+3x^4+3x²+1-(x^6+2x³+1)=x^6+3x^4+3x²+1-x^6-2x³-1=3x^4-2x³+3x²-1
f)[(x+1)²+(2-x)(2+x)]³=(x²+2x+1+4-x²)³=(2x+5)³=8x³+60x²+150x+125
g) (x²-2x)³-(x²+2x)³=x^6-6x^5+12x^4-8x³-(x^6+3x^5+12x^4+8x³)=
=x^6-6x^5+12x^4-8x³-x^6-6x^5-12x^4-8x³=-12x^5-16x³
h)(2x²-3x)³+(3x-2x²)³=8x^6-24x^5+54x^4-27x³+27x³-54x^4+36x^5-8x^6=
=12x^5