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-2x-4y-3

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-2x-4y-3

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 )