Question

分解因式（a²+b²）²-4a²b²

3a(x-y)-5b(y-x)
a的3次方b+2a²b-3ab
4a(x-y)-2b(y-x)

Answer 1

您好：

（a²+b²）²-4a²b²
=（a²+b²+2ab）（a²+b²-2ab）
=(a+b)²(a-b)²

3a(x-y)-5b(y-x)
=3a(x-y)+5b(x-y)
=(3a+5b)(x-y)

a的3次方b+2a²b-3ab
=ab(a²+2a-3)
=ab(a+3)(a-1)

4a(x-y)-2b(y-x)
=4a(x-y)+2b(x-y)
=2(x-y)(2a+b)

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Answer 2

( a" + b" )" - 4a"b"

= ( a" + b" )" - (2ab)"
= ( a" + b" + 2ab )( a" + b" - 2ab )
= ( a + b )"( a - b )"

3a(x - y) - 5b(y - x)
= 3a( x - y ) + 5b( x - y )
= ( 3a + 5b )( x - y )

(a^3)b + 2a"b - 3ab
= ab( a" + 2a - 3 )
= ab( a" + 3a - a - 3 )
= ab[ a( a + 3 ) - ( a + 3 ) ]
= ab( a - 1 )( a + 3 )

4a(x - y) - 2b(y - x)
= 4a( x - y ) + 2b( x - y )
= ( 4a + 2b )( x - y )
= 2( 2a + b )( x - y )