原式=n*(an+1)^2+(an+1)^2-n(an)^2+an*an+1
=n[(an+1)^2-(an)^2]+(an+1)^2+an*an+1
=n[(an+1)+(an)][(an+1)-(an)]+(an+1)[(an+1)+(an)] (前面平方差公式,后面合并同类项)
=[(an+1)+(an)][n*(an+1)+(an+1)-n(an)](提取公因式)
=[(an+1)+(an)][(n+1)*(an+1)-n(an)] (再合并同类项)
原式=n*(an+1)^2+(an+1)^2-n(an)^2+an*an+1
=n[(an+1)^2-(an)^2]+(an+1)^2+an*an+1
=n[(an+1)+(an)][(an+1)-(an)]+(an+1)[(an+1)+(an)] (前面平方差公式,后面合并同类项)
=[(an+1)+(an)][n*(an+1)+(an+1)-n(an)](提取公因式)
=[(an+1)+(an)][(n+1)*(an+1)-n(an)] (再合并同类项)