Question

2007²+2007²*2008²+2008² 不要 硬算

Answer 1

设A=2007

原式=A^2+A^2(A+1)^2+(A+1)^2

=A^4+2A^3+3A^2+2A+1

=A^2[A^2+2A+3+2/A+1/A^2]

=A^2[(A+1/A)^2+2(A+1/A)+1]

=A^2(A+1/A+1)^2

=(A^2+A+1)^2

代入数据得

原式=(2007^2+2007+1)^2 =4030057^2=16241359423249