12a^3b²-9a^2b+3ab
=3ab(4a²b-3a+1)
(3x+y)^2-(x-3y)^2
=(3x+y+x-3y)(3x+y-x+3y)
=(4x-2y)(2x+4y)
=4(2x+y)(x+2y)
102^2-204*98+98^2
=102²-2*102*98+98²
=(102-98)²
=4²
=16
2012^2+2012
=2012×(2012+1)
=2012×2013
∴2012^2+2012能被2012整除,也能被2013整除.
12a^3b²-9a^2b+3ab
=3ab(4a²b-3a+1)
(3x+y)^2-(x-3y)^2
=(3x+y+x-3y)(3x+y-x+3y)
=(4x-2y)(2x+4y)
=4(2x+y)(x+2y)
102^2-204*98+98^2
=102²-2*102*98+98²
=(102-98)²
=4²
=16
2012^2+2012
=2012×(2012+1)
=2012×2013
∴2012^2+2012能被2012整除,也能被2013整除.