Question

*（代表乘） ^ (代表指数）(1) 2*x^3n-1+8x^2n-1*y^n+8x^n-1*y^n(2) x^4-2x

Answer 1

(1) 2*x^3n-1+8x^2n-1*y^n+8x^n-1*y^n=2x^(n-1)(x^2n+4x^ny^n+4y^n)

(2) x^4-2x^2+x^3-X+1=x^3(x+1)-(2x-1)(x+1)=(x+1)(x^3-2x+1)=(x+1)(x-1)(x^2+x-1)

(3) a^2+b^2+c^2-2bc+2ca-2ab=(a+c)^2-2b(a+c)+b^2=(a-b+c)^2

（4） x^4+x^2y^2+y^4=(x^2+y^2)^2-(xy)^2=(x^2+xy+y^2)(x^2-xy+y^2)

(5) a^4+9a^2+81=(a^2+9)^2-9a^2=(a^2-3a+9)(a^2+3a+9)

(6) x^3+3x^2-4=(x^3-x^2)+(4x^2-4)=x^2(x-1)+4(x+1)(x-1)=(x-1)(x^2+4x+4)=(x-1)(x+2)^2