1, \(16x^3y+0,25yz^3=0,25y\left(64x^3+z^3\right)=0,25y\left(4x+z\right)\left(16x^2-4xz+z^2\right)\)
2, \(x^4-4x^3+4x^2=x^2\left(x^2-4x+4\right)=x^2\left(x-2\right)^2\)
3, \(2ab^2-a^2b-b^3=-b\left(a^2+2ab+b^2\right)=-b\left(a+b\right)^2\)
4, \(a^3+a^2b-ab^2-b^3=\left(a^3+a^2b\right)-\left(ab^2+b^3\right)=a^2\left(a+b\right)-b^2\left(a+b\right)+\left(a-b\right)\left(a+b\right)^2\)
5,\(x^3+x^2-4x-4=\left(x^3+x^2\right)-\left(4x+4\right)=x^2\left(x+1\right)-4\left(x+1\right)=\left(x-2\right)\left(x+2\right)\left(x+1\right)\)
6,\(x^3-x^2-x+1=\left(x-1\right)^3\)
7, \(x^4+x^3+x^2-1=\left(x^4+x^3\right)+\left(x^2-1\right)=x^3\left(x+1\right)+\left(x-1\right)\left(x+1\right)=\left(x+1\right)\left(x^3+x-1\right)\)
8, \(x^2y^2+1-x^2-y^2=\left(x^2y^2-x^2\right)-\left(y^2-1\right)=x^2\left(y^2-1\right)-\left(y^2-1\right)=\left(x-1\right)\left(x+1\right)\left(y-1\right)\left(y+1\right)\)
10, \(x^4-x^2+2x-1=\left(x^2\right)^2-\left(x^2-2x+1\right)=\left(x^2\right)^2-\left(x-1\right)^2=\left(x^2-x+1\right)\left(x^2+x-1\right)\)
11, \(3a-3b+a^2-2ab+b^2=\left(3a-3b\right)+\left(a^2-2ab+b^2\right)=3\left(a-b\right)+\left(a-b\right)^2=\left(a-b\right)\left(3+a-b\right)\)
12, \(a^2+2ab+b^2-2a-2b+1=\left(a+b\right)^2-2\left(a+b\right)+1=\left(a+b-1\right)^2\)
13, \(a^2-b^2-4a+4b=\left(a-b\right)\left(a+b\right)-4\left(a-b\right)=\left(a-b\right)\left(a+b-4\right)\)
5: \(x^3+x^2-4x-4\)
\(=x^2\left(x+1\right)-4\left(x+1\right)\)
\(=\left(x+1\right)\left(x-2\right)\left(x+2\right)\)
6: \(x^3-x^2-x+1\)
\(=x^2\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)^2\cdot\left(x+1\right)\)
7: \(x^4+x^3+x^2-1\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)+x^2\left(x+1\right)\)
\(=\left(x+1\right)\left(x^3+x-x^2-1+x^2\right)\)
\(=\left(x+1\right)\left(x^3+x-1\right)\)
