化简求值[(x+0.5y)^2+(x-0.5y)^2](2x^2-0.5y^2),其中x=-3,y=4.
问题描述:
化简求值[(x+0.5y)^2+(x-0.5y)^2](2x^2-0.5y^2),其中x=-3,y=4.
答
[(x+0.5y)^2+(x-0.5y)^2](2x^2-0.5y^2)
=[(x^2+xy+0.25y^2)+(x^2-xy+0.25y^2)](2x^2-0.5y^2)
=(2x^2+0.5y^2)(2x^2-0.5y^2)
=(2x^2)^2-(0.5y^2)^2
=4x^4-(1/4)y^4
将x=-3,y=4代入
原式=4*(-3)^4-(1/4)*(4)^4=260