Question

解20道因式分解题

X^3-X^2+X-1
AX+AY+X+Y
5MA+5MB-A-B
M^2-MN-5M+5N
A^2-B^2-2A+2B
M^2-N^2+2M+2N
AX^2-A^3-2AX-2A^2

Answer 1

x^3-x^2+x-1
=x^2(x-1)+(x-1)
=(x^2+1)(x-1)

ax+ay+x+y
=a(x+y)+(x+y)
=(a+1)(x+y)

5ma+5mb-a-b
=5m(a+b)-(a+b)
=(5m-1)(a+b)

m^2-mn-5m+5n
=m(m-n)-5(m-n)
=(m-5)(m-n)

a^2-b^2-2a+2b
=(a+b)(a-b)-2(a-b)
=(a+b-2)(a-b)

m^2-n^2+2m+2n
=(m+n)(m-n)+2(m+n)
=(m-n+2)(m+n)

ax^2-a^3-2ax-2a^2
=a(x+a)(x-a)-2a(x+a)
=a(x+a)(x-a-2)