分组分解法.1.x^2+3y-xy-3x2.(y+2)x^2+(y+2)x-12y-243.m^2x^2+n^2y^2-
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分组分解法.
1.x^2+3y-xy-3x
2.(y+2)x^2+(y+2)x-12y-24
3.m^2x^2+n^2y^2-m^2y^2-n^2x^2
4.x^2-4y^2-x-2y
1.x^2+3y-xy-3x
2.(y+2)x^2+(y+2)x-12y-24
3.m^2x^2+n^2y^2-m^2y^2-n^2x^2
4.x^2-4y^2-x-2y
1)X²+3Y-XY-3X
=X²-XY-(3X-3Y)
=X(X-Y)-3(X-Y)
=(X-Y)(X-3)
2)(Y+2)X²+(Y+2)X-12Y-24
=(Y+2)X²+(Y+2)X-12(Y+2)
=(Y+2)(X²+X-12)
=(Y+2)(X-3)(X+4)
3)m²X²+n²Y²-m²Y²-n²X²
=m²(X²-Y²)-n²(X²-Y²)
=(m²-n²)(X²-Y²)
=(m-n)(m+n)(X-Y)(X+Y)
4) X²-4Y²-X-2Y
=(X-2Y)(X+2Y)-(X+2Y)
=(X+2Y)(X-2Y-1)
=X²-XY-(3X-3Y)
=X(X-Y)-3(X-Y)
=(X-Y)(X-3)
2)(Y+2)X²+(Y+2)X-12Y-24
=(Y+2)X²+(Y+2)X-12(Y+2)
=(Y+2)(X²+X-12)
=(Y+2)(X-3)(X+4)
3)m²X²+n²Y²-m²Y²-n²X²
=m²(X²-Y²)-n²(X²-Y²)
=(m²-n²)(X²-Y²)
=(m-n)(m+n)(X-Y)(X+Y)
4) X²-4Y²-X-2Y
=(X-2Y)(X+2Y)-(X+2Y)
=(X+2Y)(X-2Y-1)
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