问题标题:
二分之一(a-b)+三分之四(a+b)+二分之一(a-b)-三分之一(a+b)
问题描述:
二分之一(a-b)+三分之四(a+b)+二分之一(a-b)-三分之一(a+b)
陈扬文回答:
二分之一(a-b)+三分之四(a+b)+二分之一(a-b)-三分之一(a+b)
=[二分之一(a-b)+二分之一(a-b)]+[三分之四(a+b)-三分之一(a+b)]
=(a-b)+(a+b)
=a-b+a+b
=2a
侯占强回答:
帮忙在做一道3(x+y)²-(x+y)+2(x+y)²-(x+y)³+4(x+y)
陈扬文回答:
3(x+y)²-(x+y)+2(x+y)²-(x+y)³+4(x+y)
=3(x+y)²+2(x+y)²+4(x+y)-(x+y)-(x+y)³
=5(x+y)²+3(x+y)-(x+y)³
=(x+y)[5(x+y)+3-(x+y)²]
=(x+y)[5x+5y+3-x²-2xy-y²]
=x[5x+5y+3-x²-2xy-y²]+y[5x+5y+3-x²-2xy-y²]
=5x²+5xy+3x-x³-2x²y-xy²+5xy+5y²+3y-x²y-2xy²-y³
=-x³-y³+5x²+5y²-3x²y-3xy²+10xy+3x+3y
原题那个地方怎么突然多出(x+y)³,是个立方项,结果很复杂。
陈扬文回答:
或直接展开,快一些:
3(x+y)²-(x+y)+2(x+y)²-(x+y)³+4(x+y)
=3(x+y)²+2(x+y)²+4(x+y)-(x+y)-(x+y)³
=5(x+y)²+3(x+y)-(x+y)³
=5(x²+2xy+y²)+3x+3y-(x³+3x²y+3xy²+y³)
=-x³-y³+5x²+5y²-3x²y-3xy²+10xy+3x+3y
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