1.X^2-4X2.M^3-8M^2+16M3.N^3-254.X^3-X^2-2X5.4Y^2-166.M^4-81N^47.a^4-10a^2+98.(X^2-4X)^2-(X^2-4X)-209.(X^2+9)^2-36X^210a^2-b^2-10bc-25C^211.(x^2-x)^2-4(x^2-x)+4

Question

1.X^2-4X
2.M^3-8M^2+16M
3.N^3-25
4.X^3-X^2-2X
5.4Y^2-16
6.M^4-81N^4
7.a^4-10a^2+9
8.(X^2-4X)^2-(X^2-4X)-20
9.(X^2+9)^2-36X^2
10a^2-b^2-10bc-25C^2
11.(x^2-x)^2-4(x^2-x)+4

Answer 1

1.X^2-4X
=x(x-4)
2.M^3-8M^2+16M
=m(m^2-8m+16)
=m(m-4)^2
3.N^3-25
此题错误,估计是n^2-25=(n+5)(n-5)
4.X^3-X^2-2X
=x(x^2-x-2)
=x(x-2)(x+1)
5.4Y^2-16
=4(y^2-4)
=4(y+2)(y-2)
6.M^4-81N^4
=(m^2+9n^2)(m^2-9n^2)
=(m^2+9n^2)(m+3n)(m-3n)
7.a^4-10a^2+9
=(a^2-1)(a^2-9)
=(a+1)(a-1)(a+3)(a-3)
8.(X^2-4X)^2-(X^2-4X)-20
=[(x^2-4x)-5][(x^2-4x)+4]
=[x^2-4x-5][x^2-4x+4]
=(x-5)(x+1)(x-2)^2
9.(X^2+9)^2-36X^2
=[(x^2+9)+6x][(x^2+9)-6x]
=[x^2+6x+9][x^2-6x+9]
=(x+3)^2 (x-3)^2
10.a^2-b^2-10bc-25C^2
=a^2-[b^2+10bc+25c^2]
=a^2-(b+5)^2
=(a+b+5)(a-b-5)
11.(x^2-x)^2-4(x^2-x)+4
=[(x^2-x)-2]^2
=[x^2-x-2]^2
=[(x-2)(x+1)]^2
=(x-2)^2 (x+1)^2