6道数学因式分解(1)2x(x-y)四次方-x²(x-y)²+xy(y-x)²(2)8a三
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6道数学因式分解
(1)2x(x-y)四次方-x²(x-y)²+xy(y-x)²
(2)8a三次方-b三次方
(3)4(x-y+1)+y(y-2x)
(4)3x²+5xy-2y²+x+9y+4
(5)2x²+xy-y²-4x+5y-6
(6)3x²+4xy-y²
(1)2x(x-y)四次方-x²(x-y)²+xy(y-x)²
(2)8a三次方-b三次方
(3)4(x-y+1)+y(y-2x)
(4)3x²+5xy-2y²+x+9y+4
(5)2x²+xy-y²-4x+5y-6
(6)3x²+4xy-y²
(1)
2x(x-y)^4-x²(x-y)²+xy(y-x)²
=x(x-y)²[2(x-y)²-x+y]
=x(x-y)²[2(x-y)²-(x-y)]
=x(x-y)²(x-y)[2(x-y)-1]
=x(x-y)³(2x-2y-1)
(2)
8a³-b³
=(2a)³-b³
=(2a-b)(4a²+2ab+b²)
(3)
(x-y+1)+y(y-2x)
=4x-4y+4+y²-2xy
=(y-2)²-2x(y-2)
=(y-2)(y-2-2x)
(4)
3x²+5xy-2y²+x+9y-4【题有误,最后一项应该是-4而不是+4,若被猜对请往下看】
3x²+x(5y+1)-(2y²-9y+4)
=3x²+x(5y+1)-(2y-1)(y-4)
=[3x-(y-4)][x+(2y-1)]
=(3x-y+4)(x+2y-1)
(5)
2x²+xy-y²-4x+5y-6
=2x²+(y-4)x+(-y2+5y-6)
=2x²+(y-4)x+[-(y2-5y+6)]
=2x²+(y-4)x+[-(y-2)(y-3)]
=[1x+(y-3)][2x+(-y+2)]
=(x+y-3)(2x-y+2)
(6)
3x²-4xy+y²【题目有误,应该是+y²,-y²的话无法分解,若猜对的话请往下看】
=(3x-y)(x-y)
2x(x-y)^4-x²(x-y)²+xy(y-x)²
=x(x-y)²[2(x-y)²-x+y]
=x(x-y)²[2(x-y)²-(x-y)]
=x(x-y)²(x-y)[2(x-y)-1]
=x(x-y)³(2x-2y-1)
(2)
8a³-b³
=(2a)³-b³
=(2a-b)(4a²+2ab+b²)
(3)
(x-y+1)+y(y-2x)
=4x-4y+4+y²-2xy
=(y-2)²-2x(y-2)
=(y-2)(y-2-2x)
(4)
3x²+5xy-2y²+x+9y-4【题有误,最后一项应该是-4而不是+4,若被猜对请往下看】
3x²+x(5y+1)-(2y²-9y+4)
=3x²+x(5y+1)-(2y-1)(y-4)
=[3x-(y-4)][x+(2y-1)]
=(3x-y+4)(x+2y-1)
(5)
2x²+xy-y²-4x+5y-6
=2x²+(y-4)x+(-y2+5y-6)
=2x²+(y-4)x+[-(y2-5y+6)]
=2x²+(y-4)x+[-(y-2)(y-3)]
=[1x+(y-3)][2x+(-y+2)]
=(x+y-3)(2x-y+2)
(6)
3x²-4xy+y²【题目有误,应该是+y²,-y²的话无法分解,若猜对的话请往下看】
=(3x-y)(x-y)
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