1)5x-15y
=5.(x-3y)
2)5x²y²+15x²y-30xy²
=5xy.(xy+3x-6y)
3)x.(x²-1)+3.(x²-1)
=(x+3).(x²-1)
=(x+3).(x-1).(x+1)
4)x²-10x+25
=(x)²-2.5.x+(5)²
=(x-5)²
5)x²-64
=(x)²-(8)²
=(x-8).(x+8)
6)x^4-1
=(x²)²-(1)²
=(x²-1).(x²+1)
=(x-1).(x+1).(x²+1)
7)3x.(x-1)-9.(1-x)
=3x.(x-1)+9.(x-1)
=(3x+9).(x-1)
=3.(x+3).(x-1)
8)(x-3)²-(2x+4)²
=[(x-3)-(2x+4)].[(x-3)+(2x+4)]
=(x-3-2x-4).(x-3+2x+4)
=(-x-7).(3x+1)
9)$\frac{2}{7}$x²y(x+2y)-$\frac{2}{7}$xy(x+2y)
=(x+2y).($\frac{2}{7}$x²y-$\frac{2}{7}$xy)
=(x+2y).(x-1).$\frac{2}{7}$xy
10)(2xy+1)²-(2x+y)²
=[(2xy+1)-(2x+y)].[(2xy+1)+(2x+y)]
=(2xy+1-2x-y).(2xy+1+2x+y)
=[(2xy-2x)-(y-1)].[(2xy+2x)+(y+1)]
=[2x.(y-1)-(y-1)].[2x(y+1)+(y+1)]
=(2x-1).(y-1).(2x+1).(y+1)
