分解因式4题

来源：百度知道 编辑：UC知道 时间：2024/05/25 02:03:34
1)by (y-x)^2n+b(x-y)^2n+1
2)16m^4-72m^2+81
3)-(a+1)^2-2(a^2-1)-(a-1)^2
4)x^6n+2-2x^3n+2+x^2

1)by (y-x)^(2n)+b(x-y)^(2n+1 )
=by(x-y)^(2n)+b(x-y)^(2n+1 )
=b(x-y)^(2n)*[y+(x-y)]
=b(x-y)^(2n)*x
=bx(x-y)^(2n);

2)16m^4-72m^2+81
=(4m^2)^2-2*4m^2*9+9^2
=(4m^2-9)^2
=[2m+3)(2m-3)]^2
=(2m+3)^2*(2m-3)^2;

3)-(a+1)^2-2(a^2-1)-(a-1)^2
=-[(a+1)^2+2(a+1)(a-1)+(a-1)^2]
=-[(a+1)+(a-1)]^2
=-(2a)^2
=-4a^2;

4)x^(6n+2)-2x^(3n+2)+x^2
=x^(6n)*x^2-2x^(3n)*x^2+x^2
=x^2*[x^(6n)-2x^(3n)+1]
=x^2*{[x^(3n)]^2-2*x^(3n)+1}
=x^2*[x^(3n)-1]^2
=x^2*[(x^n)^3-1^3]^2
=x^2*[(x^n-1)(x^(2n)+x^n+1]^2
=x^2*(x^n-1)^2*[x^(2n)+x^n+1]^2.

1.原式=by(y-x)^2n-b(y-x)^2n+1
=b(y-x)^2n(y-1)+1
2.原式=(4m^2-9)^2
=[(4m+3)(4m-3)]^2
3.