1.
(2a-b+3)(2a-3+b)
=[2a-(b-3)][2a+(b-3)]
=4a²-(b-3)²
=4a²-b²+6b-9
2.
20012001*4002-40024002*2001
=20012001*2001*2-2*20012001*2001
=0
3.
(a-b)x²+(a-b)xy-1/4(b-a)y ²
=(a-b)x²+(a-b)xy+1/4(a-b)y ²
=(a-b)(x²+xy+y²/4)
=(a-b)(x+y/2)²
4.(x²-2x)²+2(x²-2x)+1
=[(x²-2x)+1]²
=(x²-2x+1)²
=(x-1)^4
5.
a^8-1/256
=(a^4+1/16)(a^4-1/16)
=(a^4+1/16)(a²+1/4)(a²-1/4)
=(a^4+1/16)(a²+1/4)(a+1/2)(a-1/2)
6.先化简,在求值x=3,y=-2
2(x-y)²-(y²-x²)-(x+y)(y-x)
=2(x-y)²-(y-x)(x+y)-(x+y)(y-x)
=2(x-y)²+2(x+y)(x-y)
=2(x-y)(x-y+x+y)
=4x(x-y)
=12*5
=60