x^2(y+z)^2-2xy(x-z)(y+z)+y^2(x-z)^2 =[x(y+z)-y(x-z)]^2 =(xz+yz)^2 =z^2(x+y)^2
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x^2(y+z)^2-2xy(x-z)(y+z)+y^2(x-z)^2 =[x(y+z)-y(x-z)]^2 =(xz+yz)^2 =z^2(x+y)^2
x^2(y+z)^2-2xy(x-z)(y+z)+y^2(x-z)^2 =[x(y+z)-y(x-z)]^2 =(xz+yz)^2 =z^2(x+y)^2
x^2(y+z)^2-2xy(x-z)(y+z)+y^2(x-z)^2 =[x(y+z)-y(x-z)]^2 =(xz+yz)^2 =z^2(x+y)^2
x²(y+z)²-2xy(x-z)(y+z)+y²(x-z)² 完全平方式分解因式
[x(y+z)]²-2×x(y+z)×y(x-z)+[y(x-z)]²
-------- ------- ------- ---------
a² -2 a b + b² =(a+b)²
=[x(y+z)-y(x-z)]² 去掉里面的括号,并合并同类项
xy+xz-xy+yz=xz+yz
=(xz+yz)² 提取公因式 [z(x+y)]²
=z²(x+y)² 公式(ab)^n=a^nb^n
x^2(y+z)^2-2xy(x-z)(y+z)+y^2(x-z)^2
=[x(y+z)-y(x-z)]^2
=(xz+yz)^2
=z^2(x+y)^2