Question

Doprowadź wyrażenia do najprostszej postaci:
a. (3x-1)^3-(4x-5)(16x^2+20x+25)-(2x+5)^3
b. 7-(4x-1)^3+(5x+2)(25x^2-10x+4)
c. (2x+3)^3-(2x-3)^3-(4x^2+6x+9)(2x-3)
d. (5x-1)^3-(5x+1)^3-(25x^2-5x+1)(5x+1)

Answer 1

A. (3x-1)^3-(4x-5)(16x^2+20x+25)-(2x+5)^3=27x³-27x²+9x-1-64x³-20x²-100x+80x²+100x+125-8x³-60x²-150x-125=-45x³-27x²-141x-1


b. 7-(4x-1)^3+(5x+2)(25x^2-10x+4)=64x³-48x²+12x+1+125x³-50x²+20x+50x²-20x+8=189x³-48x²+12x+9

c. (2x+3)^3-(2x-3)^3-(4x^2+6x+9)(2x-3)=8x³+36x²+54x+27-8x³+36x²-54x+27-8x³+12x²-12x²+18x-18x+27=-8x³+72x²+81



d. (5x-1)^3-(5x+1)^3-(25x^2-5x+1)(5x+1)=
125x³-75x²+15x-1-125x³-75x²-15x-1-125x³-25x²+25x²+5x-5x-1=
-125x³-150x²-3

Answer 2

A. (3x-1)³-(4x-5)(16x²+20x+25)-(2x+5)³=
27x³-27x²+9x-1-(64x³+80x²+100x-80x²-100x-125)-(8x³+60x²+150x+125)=
27x³-27x²+9x-1-64x³-80x²-100x+80x²+100x+125-8x³-60x²-150x-125=
-45x³-87x²-141x-1
b. 7-(4x-1)³+(5x+2)(25x²-10x+4)=
7-(64x³-48x²+12x-1)+125x³-50x²+20x+50x²-20x+8=
7-64x³+48x²-12x+1+125x³-50x²+20x+50x²-20x+8=
61x³+48x²-12x+16
c. (2x+3)³-(2x-3)³-(4x²+6x+9)(2x-3)=
8x³+36x²+54x+27-(8x³-36x²+54x-27)-(8x³-12x²+12x²-18x+18x-27)=
8x³+36x²+54x+27-8x³+36x²-54x+27-8x³+12x²-12x²+18x-18x+27=
-8x³+72x²+81
d. (5x-1)³-(5x+1)³-(25x²-5x+1)(5x+1)=
125x³-75x²+15x-1-(125x³+75x²+15x+1)-(125x³+25x²-25x²-5x+5x+1)=
125x³-75x²+15x-1-125x³-75x²-15x-1-125x³-25x²+25x²+5x-5x-1=
-125x³-150x²-3