Question

因式分解：1.x^4y^4-16/1 2.xy^3-36x^3y 3.(3a+3b)^2-(a+b)^2 4.（x+2)(x-2）-x(x-2)-(2x-3)^2

5.(x+1)(x-3)-5

Answer 1

(x^4)(y^4) - 1/16
= (1/16)[ 16(xy)^4 - 1 ]
= (1/16)[ (4x"y")" - 1" ]
= (1/16)( 4x"y” - 1 )( 4x"y" + 1 )
= (1/16)( 2xy - 1 )( 2xy + 1 )( 4x"y" + 1 )

x(y^3) - 36(x^3)y
= xy( y” - 36x" )
= xy( y - 6x )( y + 6x )

( 3a + 3b )” - ( a + b )”
= ( 3a + 3b - a - b )( 3a + 3b + a + b )
= ( 2a + 2b )( 4a + 4b )
= 8( a + b )”
或者
= 3"( a + b )" - ( a + b )"
= 9( a + b )" - ( a + b )"
= 8( a + b )"

( x + 1 )( x - 3 ) - 5
= x” - 3x + x - 3 - 5
= x” - 2x - 8
= x" - 2x + 1 - 9
= ( x - 1 )” - 3"
= ( x - 1 + 3 )( x - 1 - 3 )
= ( x + 2 )( x - 4 )

( x + 2 )( x - 2 ) - x( x - 2 ) - ( 2x - 3 )"
= x" - 4 - x" + 2x - 4x" + 12x - 9
= -4x" + 14x - 13

Answer 2

1,
x^4y^4-1/16=(x²y²)²-(1/4)²=(x²y²+1/4)(x²y²-1/4)
=(x²y²+1/4)[x²y²-(1/2)²]=(x²y²+1/4)(xy+1/2)(xy-1/2)
2,
xy^3-36x^3y=xy(y²-36x²)=xy[y²-(6x)²]=xy(y+6x)(y-6x)
3,
(3a+3b)^2-(a+b)^2=[3(a+b)]²-(a+b)²=9(a+b)²-(a+b)²=8(a+b)²
4,

（x+2)(x-2）-x(x-2)-(2x-3)^2=(x-2)(x+2-x)-(2x-3)²
=2(x-2)-(2x-3)²=(2x-4)-(2x-3)²= -1+(2x-3)-(2x-3)² 题目好像有问题
5,
(x+1)(x-3)-5=x²-2x-3-5=x²-2x-8=x²-2x+1-9=(x-1)²-3²=（x-1+3)(x-1-3)
=（x+2)(x-4)