已知X-Y=A,Y-Z=B,求X方+Y方+Z方-XY-YZ-XZ的值,用含有a、b的代数式表示

x-y=a
y-z=b
相加
x-z=a+b
x²+y²+z²-xy-yz-xz
=(2x²+2y²+2z²-2xy-2yz-2xz)/2
=[(x²-2xy+y²)+(y²-2yz+z²)+(z²-2xz+x²)]/2
=[(x-y)²+(y-z)²+(z-x)²]/2
=(a²+b²+a²+2ab+b²)/2
=a²+ab+b²