证明x³-3x²+3x-1=(x-1)³
问题描述:
证明x³-3x²+3x-1=(x-1)³
答
证明:
左边=x³-3x²+3x-1
=(x³-1)-(3x²-3x)
=(x-1)(x²+x+1)-3x(x-1)
=(x-1)[(x²+x+1)-3x]
=(x-1)(x²-2x+1)
=(x-1)(x-1)²
=(x-1)³=右边
左边=右边得证!