化简多项式a-2a+3a-4a+5a-...+99a-100a用下面方法解决 a-(a+b)+(a+2b)-(a+3b)+...-(a+101b)
问题描述：
化简多项式a-2a+3a-4a+5a-...+99a-100a用下面方法解决 a-(a+b)+(a+2b)-(a+3b)+...-(a+101b)
解法1：a-2a+3a-4a+5a-..+99a-100a
=(a+3a+5a+..+99a)+(-2a-4a-6a-...-100a)
=2500a-2550a
=-50a
解法2：a-2a+3a-4a+5a-...+99a-100a
=(a-2a)+(3a-4a)+(5a-6a)+...+(99a-100a)
=-50a
答
a-(a+b)+(a+2b)-(a+3b)+...-(a+101b)
=-b+2b-3b+...-101b
=(-b+2b)+(-3b+4b)+...+(-99b+100b)-101b
=50b-101b
=-51b