几个初2的因式分解①-(x+2)^2+16(x-1)^2②-4x^n+2+12x^n+1-9x^n③(x+y)^2+10(x^2-y^2)④(x^2-6x)(x^2-6x+18)+81⑤14abx-8ab^2+2ax⑥x^2-y^2+y-0.25⑦2x-2y-x^2+y^2.我才初1这是我哥的题要有过程详写追+分！

Question

几个初2的因式分解
①-(x+2)^2+16(x-1)^2②-4x^n+2+12x^n+1-9x^n③(x+y)^2+10(x^2-y^2)④(x^2-6x)(x^2-6x+18)+81⑤14abx-8ab^2+2ax⑥x^2-y^2+y-0.25⑦2x-2y-x^2+y^2.我才初1这是我哥的题
要有过程详写追+分！

Answer 1

①-(x+2)^2+16(x-1)^2
=[4(x-1)-(x+2)][4(x-1)+(x+2)]
=(3x-6)(5x-2)
=3(x-2)(5x-2);
②-4x^(n+2)+12x^(n+1)-9x^n
=-x^n*(4x^2-12x+9)
=-x^n*(2x-3)^2;
③(x+y)^2+10(x^2-y^2)
=(x+y)^2+10(x+y)(x-y)
=(x+y)[(x+y)+10(x-y)]
=(x+y)(11x-9y);
④(x^2-6x)(x^2-6x+18)+81
=(x^2-6x)^2+18(x^2-6x)+81
=[(x^2-6x)+9]^2
=[(x-3)^2]^2
=(x-3)^4;
⑤14abx-8ab^2+2ax
=2a(7bx-4b^2+x);
⑥x^2-y^2+y-0.25
=x^2-(y^2-y+0.25)
=x^2-(y-0.5)^2
=[x-(y-0.5)][x+(y-0.5)]
=(x-y+0.5)(x+y-0.5);
⑦2x-2y-x^2+y^2
=2(x-y)-(x^2-y^2)
=2(x-y)-(x-y)(x+y)
=(x-y)[2-(x+y)]
=(x-y)(2-x-y).