试证明等式(10x+y)[10x+(10一y)]=100x(x+1)+y(10一y),并利用此等式计算98x92

题目

试证明等式(10x+y)[10x+(10一y)]=100x(x+1)+y(10一y),并利用此等式计算98x92

答案

1.因为(10x+y)[10x+(10一y)]
=100x²+100x-100xy+100xy+10y-y²
=100x²+100x+10y-y²
且100x(x+1)+y(10一y)
=100x²+100x+10y-y²
所以100x²+100x+10y-y²=100x²+100x+10y-y²
所以(10x+y)[10x+(10一y)]=100x(x+1)+y(10一y)
2.因为用(10x+y)[10x+(10一y)]=100x(x+1)+y(10一y)
所以令10x+y=98
10x+(10一y)=92
所以x=9
y=8
因为100x(x+1)+y(10一y)
所以原式为100*9*（9+1）+8*(10-8)
=9016