Question

初一因式分解题（就两道）

x^5－x^3+x^2－1
4a^2b^2－(b^2+a^2－c^2)^2

Answer 1

1. x^5－x^3+x^2－1
=x^3(x^2-1) + (x^2－1)
=(x^2－1)(x^3+1)
=(x+1)(x-1)（x+1)(x^2-x+1)
2. 4a^2b^2－(b^2+a^2－c^2)^2
=(2ab)^2-(b^2+a^2－c^2)^2
=（2ab+b^2+a^2－c^2)(2ab-b^2-a^2+c^2)
=[(a+b)^2-c^2][-(a-b)^2+c^2]
=-(a+b+c)(a+b-c)(a-b+c)(a-b-c)

Answer 2

x^5－x^3+x^2－1
=x^3(x^2-1)+(x^2-1)
=(x^2-1)(x^3+1)
=(x-1)(x+1)(x+1)(x^2-x+1)

4a^2b^2－(b^2+a^2－c^2)^2
=(2ab+b^2+a^2-c^2)(2ab-b^2-a^2+c^2)
=[(a+b)^2-c^2][c^2-(a-b)^2]
=[a+b+c][a+b-c][c+a-b][c-a+b]