1: \(5x-15y=5\left(x-3y\right)\)
6: \(x^2-64=\left(x-8\right)\left(x+8\right)\)
4: \(x^2-10x+25=\left(x-5\right)^2\)
1. \(5x-15y=5\left(x-3y\right)\)
2. \(5x^2y^2+15x^2y+30xy^2=5xy\left(xy+3x+6y\right)\)
3. \(y-x^2y-2xy^2-y^3=y\left(1-x^2-2xy-y^2\right)=y\left[1-\left(x^2+2xy+y^2\right)\right]=y\left[1-\left(x+y\right)^2\right]=y\left(1-x-y\right)\left(1+x+y\right)\)
4.\(x^2-10x+25=\left(x-5\right)^2\)
5.\(x^2-64=\left(x-8\right)\left(x+8\right)\)
6. \(125x^3+27=\left(5x+3\right)\left(25x^2+15x+9\right)\)
7. \(2xy-x^2-y^2+16=16-\left(x^2-2xy+y^2\right)=16-\left(x-y\right)^2=\left(4-x+y\right)\left(4+x-y\right)\)
8. \(\left(x-2\right)\left(x-3\right)+\left(x-2\right)-1=x^2-5x+6+x-2-1=x^2-4x+3=\left(x-1\right)\left(x-3\right)\)
9. \(3\left(x-1\right)+5\left(1-x\right)=\left(3-5\right)\left(x-1\right)=-2\left(x-1\right)\)
10. \(ax-2x-a^2+2a=x\left(a-2\right)-a\left(a-2\right)=\left(x-a\right)\left(a-2\right)\)
11. \(x^4-4\left(x^2+5\right)-25=\left(x^2-5\right)\left(x^2+5\right)-4\left(x^2+5\right)=\left(x^2+5\right)\left(x^2-9\right)=\left(x-3\right)\left(x+3\right)\left(x^2+5\right)\)
12. \(5x^2+5xy-x-y=5x\left(x+y\right)-\left(x+y\right)=\left(5x-1\right)\left(x+y\right)\)
13. \(x^3-4x^2-12x+27=\left(x^3+3x^2\right)-\left(7x^2+21x\right)+\left(9x+27\right)=\left(x^2-7x+9\right)\left(x+3\right)\)
