(x^2-1)^2-(x^2-1)(x+5)怎么因式分解

问题描述:

(x^2-1)^2-(x^2-1)(x+5)怎么因式分解

( x" - 1 )" - ( x" - 1 )( x + 5 )
= ( x" - 1 )[ ( x" - 1 ) - ( x + 5 ) ]
= ( x - 1 )( x + 1 )( x" - 1 - x - 5 )
= ( x - 1 )( x + 1 )( x" - 3x + 2x - 6 )
= ( x - 1 )( x + 1 )[ x( x - 3 ) + 2( x - 3 ) ]
= ( x - 1 )( x + 1 )( x + 2 )( x - 3 )

(x^2-1)^2-(x^2-1)(x+5)
=(x^2-1)((x^2-1)-(x+5))
=(x^2-1)(x^2-x-6)
=(x-1)(x+1)(x-3)(x+2)