Question

分解因式：ax³-ax²+ax-a

运用平方差、和提公因式法分解因式

Answer 1

ax³-ax²+ax-a
解：
原式=a(x^3-x^2+x-1)
=a(x^3+x-(x^2+1))
=a(x(x^2+1)-(x^2+1))
=a(x^2+1)(x-1)

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Answer 2

=ax²(x-1)+a(x-1)
=a(x-1)(x²+1)

Answer 3

ax³-ax²+ax-a
=ax²(x-1)+a(x-1)
=(x-1)(ax²+a)
=a(x²+1)(x-1)

Answer 4

ax³-ax²+ax-a=a(x³-x²+x-1)=a[x²(x-1)+x-1]=a(x-1)(x²+1)

Answer 5

ax³-ax²+ax-a=ax²(x-1)+a(x-1)=a(x-1)(x²+1)