1.3(a+b)^2-27c^2
=3[(a+b)^2-9c^2]
=3(a+b+3c)(a+b-3c)
2.16（x+y)^2-25（x-y)^2
=[4(x+y)]^2-[5(x-y)]^2
=(4x+4y+5x-5y)(4x+4y-5x+5y)
=(9x-y)(9y-x)
3.a^2（a-b)+b^2(b-a)
=a^2（a-b)-b^2(a-b)
=(a-b)(a^2-b^2)
=(a-b)^2(a+b)
4.(5m^2+3n^2)^2—(3m^2+5n^2)^2
=[(5m^2+3n^2)+(3m^2+5n^2)][(5m^2+3n^2)-(3m^2+5n^2)]
=(8m^2+8n^2)(2m^2-2n^2)
=16(m^2+n^2)(m^2-n^2)
=16(m^2+n^2)(m+n)(m-n)
5.a^2-144b^2
=a^2-(12b)^2
=(a+12b)(a-12b)
6.πR^2-πr^2
=π(R^2-r^2)
=π(R+r)(R-r)
7.-x^4+x^2y^2
=x^2(y^2-x^2)
=x^2(y+x)(y-x)
8.（a^2-b^2）+（3a-3b)
=(a+b)(a-b)+3(a-b)
=(a-b)(a+b+3)