若x+y=4,x^3+y^3=(x+y)(x^2-xy+y^2)z,求x^3+12xy+y^3的值.
问题描述：
若x+y=4,x^3+y^3=(x+y)(x^2-xy+y^2)z,求x^3+12xy+y^3的值.
答
x^3+12xy+y^3=(x+y)(x^2-xy+y^2)+12xy=(x+y)[(x+y)^2-3xy]+12xy
=(x+y)^3-3xy(x+y)+12xy=4^3-3xy*4+12xy=64