1: \(x^2-10x+25-y^2\)
\(=\left(x^2-10x+25\right)-y^2\)
\(=\left(x-5\right)^2-y^2\)
\(=\left(x-5-y\right)\left(x-5+y\right)\)
2: \(x^3+y^3-3x-3y\)
\(=\left(x^3+y^3\right)-3\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)-3\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2-3\right)\)
5: \(3x^3+6x^2y+3xy^2\)
\(=3x\cdot x^2+3x\cdot2xy+3x\cdot y^2\)
\(=3x\cdot\left(x^2+2xy+y^2\right)\)
\(=3x\left(x+y\right)^2\)
6: \(12x^4y^3+12x^3y^3+3x^2y^3\)
\(=3x^2y^3\cdot4x^2+3x^2y^3\cdot4x+3x^2y^3\cdot1\)
\(=3x^2y^3\left(4x^2+4x+1\right)\)
\(=3x^2y^3\left(2x+1\right)^2\)
9: \(3x^2-3y^2-12x+12y\)
\(=3\left(x^2-y^2-4x+4y\right)\)
\(=3\left[\left(x^2-y^2\right)-\left(4x-4y\right)\right]\)
\(=3\left[\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\right]\)
\(=3\left(x-y\right)\left(x+y-4\right)\)
10: \(x^2-6x-y^2+9\)
\(=\left(x^2-6x+9\right)-y^2\)
\(=\left(x-3\right)^2-y^2\)
=(x-3-y)(x-3+y)
13: \(2xy+25-y^2-x^2\)
\(=25-\left(x^2-2xy+y^2\right)\)
\(=5^2-\left(x-y\right)^2=\left(5-x+y\right)\left(5+x-y\right)\)
14: \(x^2\left(x-1\right)+16\left(1-x\right)\)
\(=x^2\left(x-1\right)-16\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-16\right)\)
\(=\left(x-1\right)\left(x-4\right)\left(x+4\right)\)
