2)
( x + 2 )( x + 3 )( x + 4 )( x + 5 ) - 24
= $( x^{2} + 7x + 10 ) ( x^{2} + 7x + 12 ) - 24$
Đặt t = $ x^{2} + 7x + 10$ ta có :
= t( t + 2 ) - 24 = $t^2$ + 2t - 24
= $t^2$ - 4t + 6t - 24 = t(t-4) + 6(t-4)
= ( t-4 )(t+6)
= ( $x^2$ + 7x + 10 - 4)( $x^2$ + 7x + 10 + 6 )
= ( $x^2$ + 7x + 6 ) ( $x^2$ + 7x + 16 )
= ( x + 1 ) ( x + 6 ) ( $x^2$ + 7x + 16 )