Rozwiązane

Wzory skróconego mnożenia oblicz:

a) (3x-1)³ - 3(× + 1) (x²-x+1) + 2(x-2)³ =
b) (2x-1)² - (2x+1)² - (x-2)(x+2) =
c) (x-2) (x² + 2x + 4) - (x-1) (x+2) =
d) (2x + 1)² - 2(x-1) (x+1) - (x-3)²

Z góry dzięki za rozwiązanie.



Odpowiedź :

a) = 27x³-27x²+ 9x-1 - 3 (x³-1)+2(x³- 6x²+12x -8) =27x³-27x²+9x-1-3x³+3+2x³-12x²+24x-16=26x³-15x²+33x-14
b) = 4x²-4x+1-4x²-4x-1-x²+4= -x² -8x +4
c) = x³+8 -(x² +2x -x -2) = x³+8 -x² -2x +x +2 = x³ -x² -x +10
d)= 4x² +4x+1 -2x² +2 -x² +6x -9= x² +10x -6
a)
(3x-1)³ - 3(x+1)(x² - x +1 ) +2 (x-2)³= (3x)³ - 3*(3x)²*1 + 3*3x*1 -1³ - 3(x³ +1³)
+ 2(x³ - 3*x²*2 +3*x*2² - 2³) = 27x³ - 27x² + 9x - 1 - 3x³ - 3 + 2x³ - 12x² + 24x - 16 = 26x³ - 39x² + 33x - 20

b)
(2x - 1)² - (2x+1)² - (x-2)(x+2) = 4x² - 2*2x*1 + 1² - (4x² + 2*2x*1 + 1²) - x² +4 = 4x² - 4x + 1 -4x² - 4x - 1 - x² + 4 = -x² - 8x + 4

c)
(x-2)(x²+2x + 4) - (x-1)(x+2) =x³ - 2³ - x² +2x - x - 2 = x³ - 8 - x² +2x - x - 2=
x³- x² - x - 10

d)
(2x+1)² -2(x-1)(x+1) - (x-3)² = 4x²+ 4x +1 -2(x² - 1) - (x² - 2*x*3 + 3²) =
4x² +4x +1 - 2x² +2 - x² + 6x - 9 = x² + 10x - 6
a)=27x³-1-3(x³-x²+x)+2(x³-8)=
=27x³-1-3x³-x²-3x+2x³-16=
=26x³-x²-4x-17
b)=4x²-1-4x²+1-x²-2x+2x-4=
x²-4
c)x³+2x³+4x-2x²-4x-8-x²-2x+1x+2=
=3x³-3x²-x-6
d)=4x²+1-2(x²-x+x-1-x²+9=
=4x²+1-2x ²-2+2x²-18=
=4x²-19