1.（x^2-3)^2+2(x^2-3)(x-3)+(x-3)^2
=(x^2-3+x-3)^2
=(x^2+x-6)^2
=(x+3)^2(x-2)^2
2.(x+1)(x+3)(x+5)(x+7)+15
=[(x+1)(x+7)][(x+3)(x+5)]+15
=(x^2+8x+7)(x^2+8x+15)+15
=(x^2+8x)+22(x^2+8x)+105+15
=(x^2+8x)+22(x^2+8x)+120
=(x^2+8x+10)(x^2+8x+12)
=(x^2+8x+10)(x+2)(x+6)
3.x^2+y^2+4x+2y+3——題目是不是寫錯(cuò)了呀
x^2-y^2+4x+2y+3
=(x^2+4x+4)-(y^2-2y+1)
=(x+2)^2-(y-1)^2
=(x+2+y-1)(x+2-y+1)
=(x+y+1)(x-y+3)
4.(a^2+a+1)^2+2(a^2+a+1)(a^2+a-1)+(a^2+a-1)^2
=(a^2+a+1+a^2+a-1)^2
=(2a^2+2a)^2
=[2a(a+1)]^2
=4a^2(a+1)^2
5.(x^2+4)^2-16x^2
=(x^2+4+4x)(x^2+4-4x)
=(x+2)^2(x-2)^2
6.(a+b+c)^2-(a-b-c)^2
=(a+b+c+a-b-c)(a+b+c-a+b+c)
=2a(2b+2c)
=4a(b+c)
7.25(x-y)^2-16(x+y)^2
=[5(x-y)+4(x+y)][5(x-y)-4(x+y)]
=(9x-y)(x-9y)
8.x^4-81x^2y^2
=x^2(x^2-9y^2)
=x^2(x+3y)(x-3y)
9.x^2(x-y)+y^2(y-x)
=(x^2-y^2)(x-y)
=(x+y)(x-y)^2
10.(a-b)(x-y)+(b-a)(x+y)
=(b-a)(-x+y+x+y)
=2y(b-a)
(乘法)
11.2(2m-1)^2-3(m+1)(m-1)-2(m-1)^2
=8m^2-8m+2-3m^2+3-2m^2+4m-2
=3m^2-4m+3
12.(2x+y+3t)(2x-y-3t)
=(2x)^2-(y+3t)^2
=4x^2-y^2-6ty-9t^2
13.(3a+1)^2(3a-1)^2
=[(3a+1)(3a-1)]^2
=(9a^2-1)^2
=81a^4-18a^2+1
14.(2x-y)(2x+y)-(3x-y)(4x-y)
=4x^2-y^2-(12x^2-7xy+y^2)
=-8x^2+7xy-2y^2
15.(-4x+2y)(-2y-4x)-(2x+3y)(8x-9y)
=(-4x)^2-(2y)^2-(16x^2+6xy-27y^2)
=16x^2-4y^2-16x^2-6xy+27y^2
=23y^2-6xy
16.(2a+b-c)^2
=(2a)^2+2·2a(b-c)+(b-c)^2
=4a^2+4ab-4ac+b^2-2bc+c^2
=4a^2+b^2+c^2+4ab-4ac-2bc