(1) 6x4y2－12x3y＋27x2y3
=3x2y·2x2y－3x2y·4x＋3x2y·9y2=3x2y(2x2y－4x＋9y2)
(2)－x4y＋x3y2－x2y3=－(x4y－x3y2＋x2y3)
=－(x2y·x2－x2y·xy＋x2y·y2)
=－x2y(x2－xy＋y2)
(3)xn＋3xn－1＋xn－2=xn－2·x2＋xn－2·3x＋xn－2·1
=xn－2(x2＋3x＋1)
(4)5(x－y)3＋10(y－x)2=5(x－y)3＋10(x－y)2
=5(x－y)2(x－y＋2)
(5)m(5ax＋ay－1)－m(3ax－ay－1)
=m[(5ax＋ay－1)－(3ax－ay－1)]
=m·(5ax＋ay－1－3ax＋ay＋1)
=m(2ax＋2ay)=2ma(x＋y)
(6)x2＋14x＋49=x2＋2·x·7＋72
=(x＋7)2
(7)(m＋n)2－6(m＋n)＋9=(m＋n－3)2
(8)－3ax2＋6axy－3ay2=－3a(x2－2xy＋y2)
=－3a(x－y)2
(9)(x2＋4)2＋8x(x2＋4)＋16x2
=(x2＋4)2＋2·(x2＋4)·4x＋(4x)2
=(x2＋4＋4x)2
=(x＋2)4
(10)64m2n2－(m2＋16n2)2
=(8mn)2－(m2＋16n2)2
=(8mn＋m2＋16n2)(8mn－m2－16n2)
=(m＋4n)2[－(m－4n)2]
=－(m＋4n)2(m－4n)2