已知x2-xy=3,xy-y2=-5,试求代数式x2+2xy-3y2的值.
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解:x2+2xy-3y2=x2-xy+3xy-3y2=x2-xy+3(xy-y2),
∵x2-xy=3,xy-y2=-5,
∴x2+2xy-3y2=3+3×(-5)=-12.
解析分析:把x2+2xy-3y2变形为x2-xy+3xy-3y2=x2-xy+3(xy-y2),然后把x2-xy=3,xy-y2=-5整体代入计算即可.
点评:本题考查了代数式求值:把所求的代数式根据已知条件进行变形,然后利用整体思想进行计算即可.