Question

利用因式分解进行计算

Answer 1

54.5²-30x16.35+4.5²
=54.5²-2x54.5x15x0.3+4.5²
=(54.5-4.5)²
=50²
=2500

Answer 2

（1-1/2²）×（1-1/3²）×（1-1/4²）×……（1-1/2013²）
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/2013)(1+2013)
=1/2x3/2x2/3x4/3x3/4x5/4x...x2012/2013x2014/2013
=1/2 x 2014/2013
=1007/2013