Question

1.a^4-4a^3+4a^2-16

Answer 1

1.

a^4-4a^3+4a^2-16

=a^2(a^2-4a+4)-16

=a^2(a-2)^2-16 (利用平方差公式)

=(a(a-2)+4)(a(a-2)-4)

=(a^2-2a+4)(a^2-2a-4)

2.

a^2+b^2+c^2-2ab-2bc+2ac

=(a^2+c^2+2ac)+b^2-2ab-2bc (先减b^2,再加b^2)

=(a+c)^2-b^2+(2b^2-2ab-2bc)

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

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

=(a+c-b)^2

3.

9a^2-x^2-16b^2-8bx-6a+1

=(9a^2-6a+1)-(x^2+8bx+16b^2)

=(3a-1)^2-(x+4b)^2

=(3a-1+x+4b)(3a-1-x-4b)

4.有一点问题吧,这个z好像没什么关系啊.

5.

x^3-2x^2y+xy^2-4x^2+4xy+4x

=x(x^2-2xy+y^2-4x+4y+4)

=x(x-y-2)^2

其中最后一步用到了与第二题类似的方法,只需将y看作a,x看作b,2看作c即可