Question

初二数学分解因式(x+1)(x-2)(x+3)(x+6)-16急啊,

Answer 1

( x + 1 )( x - 2 )( x + 3 )( x + 6 ) - 16

不用急于展开括号

= ( x + 1 )( x + 3 )( x + 6 )( x - 2 ) - 16

= ( x" + 3x + x + 3 )( x" - 2x + 6x - 12 ) - 16

= ( x" + 4x + 3 )( x" + 4x - 12 ) - 16

= ( x" + 4x )" + 3( x" + 4x ) - 12( x" + 4x ) - 36 - 16

= ( x" + 4x )" - 9( x" + 4x ) - 52

= ( x" + 4x )" - 13( x" + 4x ) + 4( x" + 4x ) - 52

= ( x" + 4x )( x" + 4x - 13 ) + 4( x" + 4x - 13 )

= ( x" + 4x + 4 )( x" + 4x - 13 )

= ( x + 2 )"( x" + 4x - 13 )