作业帮因式分解(1)2x^(n+1)-3x^ny+2x^(n-1)-3x^(n-2)y(2)3ax+4by+4ay+3by(3
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/22 06:38:20
因式分解
(1)2x^(n+1)-3x^ny+2x^(n-1)-3x^(n-2)y
(2)3ax+4by+4ay+3by
(3)(ax+by)^2+(bx-ay)^2
(4)m^2+5n-mn-5m
(1)2x^(n+1)-3x^ny+2x^(n-1)-3x^(n-2)y
(2)3ax+4by+4ay+3by
(3)(ax+by)^2+(bx-ay)^2
(4)m^2+5n-mn-5m
2x^(n+1) - 3(x^n)y + 2x^(n-1) - 3x^(n-2)y
= x^(n-2)[ 2x"' - 3x"y + 2x - 3y ]
= x^(n-2)[ 2x( x" + 1 ) - 3y( x" + 1 ) ]
= [ x^(n-2) ]( x" + 1 )( 2x - 3y )
3ax + 4by + 4ay + 3by
= 3ax + 4ay + 7by
不能分解因式
( ax + by )" + ( bx - ay )"
= a"x" + b"y" + 2abxy + b"x" + a"y" - 2abxy
= x"( a" + b" ) + ( a" + b" )y"
= ( a" + b" )( x" + y" )
m" + 5n - mn - 5m
= m" - mn - 5m + 5n
= m( m - n ) - 5( m - n )
= ( m - n )( m - 5 )
= x^(n-2)[ 2x"' - 3x"y + 2x - 3y ]
= x^(n-2)[ 2x( x" + 1 ) - 3y( x" + 1 ) ]
= [ x^(n-2) ]( x" + 1 )( 2x - 3y )
3ax + 4by + 4ay + 3by
= 3ax + 4ay + 7by
不能分解因式
( ax + by )" + ( bx - ay )"
= a"x" + b"y" + 2abxy + b"x" + a"y" - 2abxy
= x"( a" + b" ) + ( a" + b" )y"
= ( a" + b" )( x" + y" )
m" + 5n - mn - 5m
= m" - mn - 5m + 5n
= m( m - n ) - 5( m - n )
= ( m - n )( m - 5 )
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