a) -x³ + 3x² - 3x + 1
= - (x³ - 3x² + 3x - 1)
= - [(x)³ - 3.(x)².1 + 3.x.(1)² - (1)³]
= - (x - 1)³
b) 8 - 12x + 6x² - x³
= (2)³ - 3.(2)².x + 3.2.(x)² - (x)³
= (2 - x)³
c) x³ + x² + $\frac{x}{3}$ + $\frac{1}{27}$
= (x)³ + 3.(x)².$\frac{1}{3}$ + 3.x.($\frac{1}{3}$)² + ($\frac{1}{3}$)³
= (x + $\frac{1}{3}$)³
d) 8x³ + 12x² + 6x + 1
= (2x)³ + 3.(2x)².1 + 3.2x.(1)² + (1)³
= (2x + 1)³
e) x³ - 6x²y + 12xy² - 8y³
= (x)³ - 3.(x)².2y + 3.x.(2y)² - (2y)³
= (x - 2y)³
f) x³ + $\frac{3}{2}$x² + $\frac{3}{4}$x + $\frac{1}{8}$
= (x)³ + 3.(x)².$\frac{1}{2}$ + 3.x.($\frac{1}{2}$)² + ($\frac{1}{2}$)³
= (x + $\frac{1}{2}$)³
