a) \(15xy-20x^2=5.\left(3xy-4x^2\right)\)

b) \(\left(x-4\right)^2-\left(y-5\right)^2\)

= \(\left(x-4-y+5\right).\left(x-4+y-5\right)\)

= \(\left(x-y+1\right).\left(x+y-9\right)\)

c) \(x^4-9x^3-x^2+9x\)

= \(x^3.\left(x-9\right)-x.\left(x-9\right)\)

= \(\left(x-9\right).\left(x^3-x\right)=\left(x-9\right).x.\left(x^2-1\right)\)

= \(\left(x-9\right).x.\left(x-1\right).\left(x+1\right)\)

d) \(2x^2-7x+5\)

= \(2x^2-2x-5x+5\)

= \(2x.\left(x-1\right)-5.\left(x-1\right)\)

= \(\left(x-1\right).\left(2x-5\right)\)

e) \(\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+15\)

= \(\left(x^2+8x+7\right).\left(x^2+8x+15\right)+15\) (*)

ĐẶT \(x^2+8x+7\) = a

Phương trình (*) \(\Leftrightarrow a\left(a+8\right)+15\)

= \(a^2+8a+15\)

= \(\left(a+3\right)\left(a+5\right)\)

\(=\left(x^2+8x+7+3\right)\left(x^2+8x+7+5\right)\)

= \(\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)

= \(\left(x^2+8x+10\right)\left(x+2\right)\left(x+6\right)\)