Question

一些初中的因式分解的题目，求大神解答！

x4-5x2+4
4x4-65x2y2+16y4
a6-7a3b3-8b6
6a4-5a3-4a2

4a6-37a4b2+9a2b4
（x2-3）2-4x2
x2（x-2）2-9
（3x2+2x+1）2-（2x2+3x+3)2
(x2+x)2+17(x2+x)+60
(x2+xy+y2)(x2+xy+2y2)-12y4
x2-2xy-3y2+2x+10y-8
(a-b)x2+2ax+a+b

Answer 1

x^4 - 5x" + 4
= (x")" - x" - 4x" + 4
= x"( x" - 1 ) - 4( x" - 1 )
= ( x" - 1 )( x" - 4 )
= ( x - 1 )( x + 1 )( x - 2 )( x + 2 )

4x^4 - 65x"y" + 16y^4
= 4x^4 - x"y" - 64x"y" + 16y^4
= x"( 4x" - y" ) - 16y"( 4x" - y" )
= ( x" - 16y" )( 4x" - y" )
= ( x - 4y )( x + 4y )( 2x - y )( 2x + y )

a^6 - 7a"'b"' - 8b^6
= a^6 - 8a"'b"' + a"'b"' - 8b^6
= a"'( a"' - 8b"' ) + b"'( a"' - 8b"' )
= ( a"' + b"' )( a"' - 8b"' )
= ( a + b )( a" - ab + b" )( a - 2b )( a" + 2ab + 4b" )
= ( a + b )( a - 2b )( a" - ab + b" )( a" + 2ab + 4b" )

6a^4 - 5a"' - 4a"
= a"( 6a" - 5a - 4 )
= a"( 6a" + 3a - 8a - 4 )
= a"[ 3a( 2a + 1 ) - 4( 2a + 1 ) ]
= a"( 2a + 1 )( 3a - 4 )

4a^6 - 37a^4b" + 9a"b^4
= a"( 4a^4 - 37a"b" + 9b^4 )
= a"( 4a^4 - a"b" - 36a"b" + 9b^4 )
= a"[ a"( 4a" - b" ) - 9b"( 4a" - b" ) ]
= a"( a" - 9b" )( 4a" - b" )
= a"( a + 3b )( a - 3b )( 2a + b )( 2a - b )

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

x"( x - 2 )" - 9
= x"( x - 2 )" - 3"
= ( x" - 2x + 3 )( x" - 2x - 3 )
= ( x - 1 )( x + 1 )( x - 3 )( x + 3 )

( 3x" + 2x + 1 )" - ( 2x" + 3x + 3 )"
= ( 3x" + 2x + 1 + 2x" + 3x + 3 )( 3x" + 2x + 1 - 2x" - 3x - 3 )
= ( 5x" + 5x + 4 )( x" - x - 2 )
= ( 5x" + 5x + 4 )( x" + x - 2x - 2 )
= ( 5x" + 5x + 4 )[ x( x + 1 ) - 2( x + 1 ) ]
= ( 5x" + 5x + 4 )( x + 1 )( x - 2 )

( x" + x )" + 17( x" + x ) + 60
= ( x" + x )" + 12( x" + x ) + 5( x" + x ) + 60
= ( x" + x )( x" + x + 12 ) + 5( x" + x + 12 )
= ( x" + x + 5 )( x" + x + 12 )

( x" + xy + y" )( x" + xy + 2y" ) - 12y^4
= ( x" + xy + y" )( x" + xy + y" + y" ) - 12y^4
= ( x" + xy + y" )" + y"( x" + xy + y" ) - 12y^4
= ( x" + xy + y" )" + 4y"( x" + xy + y" ) - 3y"( x" + xy + y" ) - 12y^4
= ( x" + xy + y" )( x" + xy + y" + 4y" ) - 3y"( x" + xy + y" + 4y" )
= ( x" + xy + y" - 3y" )( x" + xy + y" + 4y" )
= ( x" + xy - 2y" )( x" + xy + 5y" )
= ( x" + 2xy - xy - 2y" )( x" + xy + 5y" )
= [ x( x + 2y ) - y( x + 2y ) ]( x" + xy + 5y" )
= ( x - y )( x + 2y )( x" + xy + 5y" )

x" - 2xy - 3y" + 2x + 10y - 8
= x" - 2xy + y" - 4y" + 2x - 2y + 12y - 8
= ( x - y )" + 2( x - y ) + 1 - 4y" + 12y - 9
= [ ( x - y ) + 1 ]" - [ ( 2y )" - 6( 2y ) + 3" ]
= ( x - y + 1 )" - ( 2y - 3 )"
= ( x - y + 1 + 2y - 3 )( x - y + 1 - 2y + 3 )
= ( x + y - 2 )( x - 3y + 4 )

( a - b )x" + 2ax + a + b
= ax" + 2ax + a - bx" + b
= a( x" + 2x + 1 ) - b( x" - 1 )
= a( x + 1 )" - b( x - 1 )( x + 1 )
= ( x + 1 )[ ( ax + a ) - ( bx - b ) ]
= ( x + 1 )( ax - bx + a + b )

Answer 2

x4-5x2+4=（x^2-1）4（x^2-4)
4x4-65x2y2+16y4=2X^2+4y^2-9x^2y^2）（2X^2+4y^2+9x^2y^2）
a6-7a3b3-8b6不会
6a4-5a3-4a2=a^2（2x+1）（3x-4）
4a6-37a4b2+9a2b4不会
（x2-3）2-4x2=（x2-3-2x）（x2-3+2x）
x2（x-2）2-9=〔x（x-2)-3〕〔x（x-2)+3〕
（3x2+2x+1）2-（2x2+3x+3)2=(x^2-x-2)(5x^2+5x+4)

Answer 3

能拍下来吗

追问

大概不行QAQ

Answer 4

不是方程，怎么解？

追问

因式分解啊……题目就是这样的【摊手

追答

好嘛，不过都有人帮你解了，你自己去参考吧，谢谢