Question

因式分解 一、（x平方+x-2）（x平方+x-12） 二、（x平方-1）（x+3）（x+5）+15 三、x平方-y平方-

Answer 1

( x" + x - 2 )( x" + x - 12 )

= ( x" + 2x - x - 2 )( x" + 4x - 3x - 12 )

= [ x ( x + 2 ) - ( x + 2 ) ][ x( x + 4 ) - 3( x + 4 ) ]

= ( x - 1 )( x + 2 )( x - 3 )( x + 4 )

( x" - 1 )( x + 3 )( x + 5 ) + 15

= ( x" - 1 )( x" + 8x + 15 ) + 15

= x"( x" + 8x + 15 ) - x" - 8x - 15 + 15

= x"( x" + 8x ) + 15x" - x" - 8x

= x"( x" + 8x ) + 16x" - 2x" - 8x

= x"( x" + 8x + 16 ) - 2x( x + 4 )

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

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

x" - y" - 2x - 4y - 3

= x" - 2x + 1 - y" - 4y - 4

= ( x" - 2x + 1 ) - ( y" + 4y + 4 )

= ( x - 1 )" - ( y + 2 )"

= ( x - 1 + y + 2 )( x - 1 - y - 2 )

= ( x + y + 1 )( x - y - 3 )