`(x+2)(x+3)(x+4)(x+5) - 24`
` = [ (x+2) (x+5)] . [ (x+3)(x+4)] -24`
` = (x^2 + 5x + 2x +10) (x^2 + 4x +3x + 12) - 24`
` = (x^2 + 7x + 10)(x^2 + 7x + 12) - 24`
` = [ (x^2 + 7x + 11) - 1] . [ (x^2 + 7x + 11) + 1] - 24`
` = (x^2 + 7x + 11)^2 - 1 - 24`
` = (x^2 + 7x + 11)^2 - 25`
` = (x^2+ 7x+11)^2 -5^2`
`= (x^2 + 7x + 11 - 5)(x^2 + 7x + 11 + 5)`
` = (x^2 + 7x + 6)(x^2 + 7x + 16)`
` = (x^2 + x +6x + 6)(x^2 + 7x + 16)`
` = [ x(x+1) + 6(x+1)]. (x^2 + 7x + 16)`
` = (x+6)(x+1)(x^2 + 7x+16)`
