Question

已知a=2008x+2009,b=2008x+2008 c=2008x+2007求代数式2a^2-2ab+2b^2-2b

Answer 1

2a^2-2ab+2b^2-2bc+2c^2-2ac

=(a^2-2ab+b^2)+a^2+b^2-2bc+c^2-2ac+c^2

=(a^2-2ab+b^2)+(a^2-2ac+c^2)+(b^2-2bc+c^2)

=(a-b)^2+(a-c)^2+(b-c)^2

=(2008x+2009-2008x-2008 )^2+(2008x+2009-2008x-2007)^2+(2008x+2008 -2008x-2007)^2

=1+2^2+1

=6