1.
5m^2(a-b-c)+20m^4(b+c-a)
=5m^2(a-b-c)-20m^4(a-b-c)
=5m^2(a-b-c)(1-4m^2)
=5m^2(a-b-c)(1+2m)(1-2m)
2.
a^4-1/2a^2x^2y^2+1/16x^4y^4
=(a^2-1/4x^2y^2)^2
=(a+1/2xy)^2(a-1/2xy)^2
3.
9(x+3y)^2-25(x-3y)^2
=[3(x+3y)+5(x-3y)][3(x+3y)-5(x-3y)]
=(8x-6y)(-2x+6y)
=(-4)(4x-3y)(x-3y)
4.
4(2x-y)^2+21-12(2x-y+1)
=4[(2x-y+1)-1]^2-12(2x-y+1)+21
=4(2x-y+1)^2-8(2x-y+1)+4-12(2x-y+1)+21
=4(2x-y+1)^2-20(2x-y+1)+25
=[2(2x-y+1)-5]^2
=(4x-2y-3)^2