Question

因式分解题目~

x^2n+6x^n-y²+9
x²(x²+y²)-2y^4
x²+3x-(a²+a-2)
m³+4m^4-5-20m
a^4-27a²b²+b^4
球过程
诶 这是5道题的说 分别做……

Answer 1

x^2n+6x^n-y²+9
=(x^n+3)²-y²
=(x^n+3+y)(x^n+3-y)

x²(x²+y²)-2y^4
=x^4+x²y²-2y^4
=(x²+2y²)(x²-y²)
=(x²+2y²)(x+y)(x-y)

x²+3x-(a²+a-2)
=不能分解

m³+4m^4-5-20m
=m³(4m+1)-5(4m+1)
=(4m+1)(m³-5)

a^4-27a²b²+b^4
=(a²-b²)²-25a²b²
=(a²+5ab-b²)(a²-5ab-b²)

Answer 2

x^2n+6x^n-y²+9
=x^2n+6x^n+9-y²
=(x^n+3)²-y²
=(x^n+3-y)(x^n+3+y)

x²(x²+y²)-2y^4
=x^4+x²y²-2y^4
=(x²+2y²)(x²-y²)
=(x²+2y²)(x-y)(x+y)

x²+3x-(a²+a-2)
不可以因式分解

m^3+4m^4-5-20m
=m^3(1+4m)-5(1+4m)
=(m^3-5)(1+4m)

a^4-27a²b²+b^4
=a^4+2a²b²+b^4-29a²b²
=(a²+b²)²-29a²b²
=(a²+b²-ab√29)(a²+b²+ab√29)

Answer 3

x^2n+6x^n-y²+9
=(x^n+3)^2-y^2
=(x^n+3+y)(x^n+3-y)

x²(x²+y²)-2y^4
=x^4+x^2y^2-2y^4
=(x^2+2y^2)(x^2-y^2)
=(x^2+2y^2)(x+y)(x-y)

x²+3x-(a²+a-2)
=x^2+3x-(a+2)(a-1)
=(x+a+2)*(x-a+1)

m³+4m^4-5-20m
=m^3(1+4m)-5(1+4m)
=(m^3-5)(1+4m)

a^4-27a²b²+b^4
=a^4-2a²b²+b^4-25a²b²
=(a^2-b^2)^2-25a²b²
=(a^2-b^2+5ab)(a^2-b^2-5ab)