因式分解2題

所用公式：
a² - b² = (a + b)(a - b)
a³ - b³ = (a - b)(a² +ab + b²)
a³ + b³ = (a + b)(a² -ab + b²)


1.
令 u = (x + y)³
則 x³ - (x + y)³
= x³ - u³
= (x - u)(x² + xu + u²)
= [x - (x + y)] [x² + x(x + y) + (x+ y)²]
= (x - x - y)(x² + x² + xy + x² + 2xy + y²)
= -y(3x² + 3xy + y²)


2.
1 - 729x⁶
= (1³)² - [(3x)³]²
= [1³ + (3x)³] [1³ - (3x)³]
= (1 + 3x)[1² - 1(3x) + (3x)²](1 - 3x)[1² + 1(3x) + (3x)²]
= (1 + 3x)(1 - 3x)(1 - 3x + 9x²)(1 + 3x + 9x²)