因式分解：(x+y)(x+y)(x+y) 计算:999的立方+3×999的平方+3×999+1
问题描述：
因式分解：(x+y)(x+y)(x+y) 计算:999的立方+3×999的平方+3×999+1
答
(x+y)(x+y)(x+y)=(x+y)^3
999的立方+3×999的平方+3×999+1
=999的立方+2×999的平方+999+999的平方+2×999+1
=999(999+1)^2+(999+1)^2
=999*1000000+1000000
=1000000000
答
(x+y)(x+y)(x+y)
=(x+y)[x(x+y)+y(x+y)]
=(x+y)(x²+xy+xy+y²)
=(x+y)(x²+2xy+y²)
=x(x²+2xy+y²)+y(x²+2xy+y²)
=x³+2x²y+xy²+x²y+2xy²+y³
=x³+3x²y+3xy²+y³
999³+3×999²+3×999+1
=(999+1)(999+1)(999+1)
=1000×1000×1000
=1000000000
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