因式分解：(a+b)^3-(a+b)

题目

因式分解：(a+b)^3-(a+b)
a^2(x-y)^2-b^2(y-x)^2
(5a^2-2b^2)^2-(2a^2-5b^2)^2
用简便方法计算：
57^2×0.01-43^2×0.01

答案

( a + b )"' - ( a + b )
= ( a + b )[ ( a + b )" - 1 ]
= ( a + b )[ ( a + b )" - 1" ]
= ( a + b )( a + b + 1 )( a + b - 1 )
a"( x - y )" - b"( y - x )"
= [ a( x - y ) ]" - [ b( x - y ) ]"
= [ ( ax - ay ) + ( bx - by ) ][ ( ax - ay ) - ( bx - by ) ]
= ( ax - ay + bx - by )( ax - ay - bx + by )
( 5a" - 2b" )" - ( 2a" - 5b" )"
= [ ( 5a" - 2b" ) + ( 2a" - 5b" ) ][ ( 5a" - 2b" ) - ( 2a" - 5b" ) ]
= ( 5a" - 2b" + 2a" - 5b" )( 5a" - 2b" - 2a" + 5b" )
= ( 7a" - 7b" )( 3a" + 3b" )
= 21( a" + b" )( a + b )( a - b )
57" X 0.01 - 43" X 0.01
= 5.7" - 4.3"
= ( 5.7 - 4.3 )( 5.7 + 4.3 )
= 1.4 X 10
= 14
或者
= 0.01 X ( 57" - 43" )
= 0.01 X ( 57 + 43 )( 57 - 43 )
= 0.01 X 100 X 14
= 14