计算(x+2y+z)(x+2y-z),(5x+2y)(5x-2y)
问题描述：
计算(x+2y+z)(x+2y-z),(5x+2y)(5x-2y)
答
(1) (x+2y+z)(x+2y-z) =x(x+2y-z)+2y(x+2y-z)+z(x+2y-z) =x^2+2xy-xz + 2xy+4y^2-2yz + xz+2yz-z^2 =x^2+4y^2-z^2+4xy 或者直接平方差公式：(x+2y+z)(x+2y-z) =(x+2y)^2-z^2 =x^2+4y^2-z^2+4xy (2):(5x+2y)(5x-2y)=(5x)^2-(2y)^2=25x^2-4y^2