(2x+1)^2-(x-1)^2
= (4x^2 + 4x +1) - (x^2 - 2x +1)
= 2x^2 + 6x
= 2x(x+3)
9(x+5)^2-(x-7)^2
= 9 (x^2 + 10x + 25) - (x^2 - 14x +49)
= 9x^2 + 90x + 225 - x^2 + 14x - 49
= 8x^2 + 104x + 176
= 8x^2 + 8 * 13x + 8 * 22
= 8(x^2 + 13x +22)
x^2-y^2-x+y
= (x^2 - y^2) - (x-y)
= (x-y) (x+y) - (x-y)
= (x-y) (x+y+1)