1.n(n+3)(n+1)(n+2)+1=(n^2+3n)(n^2+3n+2)+1
=(n^2+3n)^2+2(n^2+3n)+1=(n^2+3n+1)^2
2.(x^2+8x+7)(x^2+8x+15)+15=(x^2+8x+7)^2+8(x^2+8x+7)+15
=(x^2+8x+12)(x^2+8x+10)
=(x+2)(x+6)(x^2+8x+10)
3.x^2+3xy+2y^2+4x+5y+3=(x+y+a)(x+2y+b)
解出,a=1,b=3
所以,x^2+3xy+2y^2+4x+5y+3=(x+y+1)(x+2y+3)
这是一种待定系数法
4.12*A^((3N+1)-32*A^(2N-1)+24*A^(N-1)
=4A^(N-1)[3A^(2N+1)-8*A^N+6]