7) Rozłóż wyrażenia na czynniki stosując wzory skróconego mnożenia:
a) x³ - 3x² + 3x - 1 =
b) x³ + 18x² +108x +216 =
c) 27- 27y + 9y² - y³ =
d) 8x³ + 36x²y +54xy² +27y³ =
e) 1 + 6x+ 12x² +8x =
f) 1- 15y + 75y² - 125y³ =
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a) x³-3x²+3x-1 = =x³−x²−2x²+2x+x−1=x²(x−1)−2x(x−1)+(x−1)=
=(x−1)(x²−2x+1)=(x−1)(x−1)²=(x−1)³
b) x³ + 18x² +108x +216 =x³+3*x²*6+3*x*6²+6³=(x+6)³
c) 27- 27y + 9y² - y³ =3³-3*3²y+3*3y²-y³=(3-y)³
d) 8x³ + 36x²y +54xy² +27y³ =(2x)³+3*(2x)²*(3y)+3*(2x)*(3y)²+(3y)³=(2x+3y)³
e) 1 + 6x+ 12x² +8x =1³+3*(2x)*1²+3*(2x)²*1+(2x)³=(2x+1)³
f) 1- 15y + 75y² - 125y³ =1³−3*(5y)*1²+3*(5y)²*1−(5y)³=(1−5y)³