分解因式：（x+y)(x-y)+2x+1

（x+y)(x-y)+2x+1
=x²-y²+2x+1
=(x²+2x+1)-y²
=(x+1)²-y²
=(x+y+1)(x-y+1)

（x+y)(x-y)+2x+1
=x^2-y^2+2x+1
=(x+1)^2-y^2
=(x+1-y)(x+1+y)

（x+y)(x-y)+2x+1
解：原式=x^2-xy+xy-y^2+2x+1
=x^2-y^2+2x+1
=(x^2+2x+1)-y^2
=(x+1)^2-y^2
=[(x+1)+y][(x+1)-y]
=(x+y+1)(x-y+1)
注：x^2是 x平方的意思，这是电脑上的写法

（x+y)(x-y)+2x+1
=x^2-y^2+2x+1
=（x+1）^2-y^2
=(x+1+y)(x+1-y)