因式分解 :x^3-25x; -4x^3+4x^3-x^3; x^2(x-y)-y^2(x-y); (x-1)(x-3)+1

问题描述:

因式分解 :x^3-25x; -4x^3+4x^3-x^3; x^2(x-y)-y^2(x-y); (x-1)(x-3)+1

x^3-25x;=x(x²-25)=x(x-5)(x+5)-4x^3+4x^3-x^3;= -x³x^2(x-y)-y^2(x-y)=(x-y)(x²-y²)=(x-y)²(x+y)(x-1)(x-3)+1=x²-4x+4=(x-2)²