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1:A^4-7A^2+12:(X-Y)(X-2Y)-6Y^23:(X^2+3X-3)(X^2+3X+4)4:(X^2-7X+6)(X^2-X-6)+565:X^2-2XY-3Y^2+3X-5Y+2
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答案和解析
1.A^4-7A^2+1=a^4+2a^2+1-9a^2
=(a^2+1)^2-9a^2
=(a^2+3a+1)(a^2-3a+1)
2.(X-Y)(X-2Y)-6Y^2=X^2-3XY-4Y^2
=(X+Y)(X-4Y）
3.（X^2+3X-3)(X^2+3X+4)-8
=(x^2+3x)^2 -3(x^2+3x)+4(x^2+3x)-12-8
=(x^2+3x)+(x^2+3x)-20
=(x^2+3x+5)(x^2+3x-4)
=(x^2+3x+5)(x+4)(x-1)
4.(X^2-7X+6)(X^2-X-6)+56=(x-6)(x-1)(x-3)(x+2)+56
=[(x-6)(x+2)][(x-1)(x-3)]+56
=(x^2-4x-12)(x^2-4x+3)+56
=(x^2-4x)^2-9(x^2-4x)-36+56
=(x^2-4x)^2-9(x^2-4x)+20
=(x^2-4x-4)(x^2-4x-5)
=(x^2-4x-4)(x-5)(x+1)
5.X^2-2XY-3Y^2+3X-5Y+2=(x-3y)(x+y)+3x-5y+2
=(x-3y+1)(x+y+2)
=(a^2+1)^2-9a^2
=(a^2+3a+1)(a^2-3a+1)
2.(X-Y)(X-2Y)-6Y^2=X^2-3XY-4Y^2
=(X+Y)(X-4Y）
3.（X^2+3X-3)(X^2+3X+4)-8
=(x^2+3x)^2 -3(x^2+3x)+4(x^2+3x)-12-8
=(x^2+3x)+(x^2+3x)-20
=(x^2+3x+5)(x^2+3x-4)
=(x^2+3x+5)(x+4)(x-1)
4.(X^2-7X+6)(X^2-X-6)+56=(x-6)(x-1)(x-3)(x+2)+56
=[(x-6)(x+2)][(x-1)(x-3)]+56
=(x^2-4x-12)(x^2-4x+3)+56
=(x^2-4x)^2-9(x^2-4x)-36+56
=(x^2-4x)^2-9(x^2-4x)+20
=(x^2-4x-4)(x^2-4x-5)
=(x^2-4x-4)(x-5)(x+1)
5.X^2-2XY-3Y^2+3X-5Y+2=(x-3y)(x+y)+3x-5y+2
=(x-3y+1)(x+y+2)
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