am-an-mˆ2+nˆ2aˆ2-9bˆ2+2a-6ba(a-1)(a-2)-6已知xˆ2+10xy+25yˆ2-1=0,化简xˆ3+5xˆ2y+xˆ2

am-an-mˆ2+nˆ2aˆ2-9bˆ2+2a-6ba(a-1)(a-2)-6已知xˆ2+10xy+25yˆ2-1=0,化简xˆ3+5xˆ2y+xˆ2
am-an-mˆ2+nˆ2
aˆ2-9bˆ2+2a-6b
a(a-1)(a-2)-6
已知xˆ2+10xy+25yˆ2-1=0,化简xˆ3+5xˆ2y+xˆ2

am-an-mˆ2+nˆ2aˆ2-9bˆ2+2a-6ba(a-1)(a-2)-6已知xˆ2+10xy+25yˆ2-1=0,化简xˆ3+5xˆ2y+xˆ2
1.am-an-mˆ2+nˆ2
=a(m-n)-(m-n)(m+n)
=(m-n)(a-m-n)
2.aˆ2-9bˆ2+2a-6b
=(a+3b)(a-3b)+2(a-3b)
=(a-3b)(a+3b+2)
3.a(a-1)(a-2)-6
=aˆ3-3aˆ2+2a-6
=aˆ2(a-3)+2(a-3)
=(aˆ2+2)(a-3)
4.因为xˆ2+10xy+25yˆ2-1=0
所以（x+5y）ˆ2=1
x+5y=1或x+5y=-1
xˆ3+5xˆ2y+xˆ2
=xˆ2(x+5y+1)
所以当x+5y=1时,原式=2xˆ2
当x+5y=-1时,原式=0

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