分解因式16(2x-y)^2-(x+y)^2简便计算999.5^2-0.5^2
问题描述：
分解因式16(2x-y)^2-(x+y)^2
简便计算999.5^2-0.5^2
答
16(2x-y)^2-(x+y)^2
=[4(2x-y)+(x+y)][(4(2x-y)-(x+y)]
=(9x-3y)(7x-5y)
=3(3x-y)(7x-5y)
999.5^2-0.5^2
=(999.5+0.5)(999.5-0.5)
=1000x999
=999000
答
16(2x-y)^2-(x+y)^2=[4(2x-y)]^2 - (x+y)^2=[4(2x-y) + (x+y)]*[4(2x-y) - (x+y)]=(9x-3y)(7x-5y)=3(3x-y)(7x-5y)999.5^2-0.5^2=(999.5+0.5)*(999.5-0.5)=1000*999=999000