Question

简便计算 2014³-2012³-6×2014²+12×2013

Answer 1

令a=2014

2012=a-2

2013=a-1

a^3-(a-2)^3-6a^2+12(a-1)

立方差公式

=(a-a+2)[a^2+a(a-2)+(a-2)^2]-(6a^2-12a+12)

=2(a^2+a^2-2a+a^2-4a+4)-6(a^2-2a+2)

=2(3a^2-6a+4)-6a^2+12a-12

=6a^2-12a+8-6a^2+12a-12

=-4