Question

分解因式

4xy²-4x²y-y³=？3x³-18x²+27x=？（a-b）²-12（a-b）c+36c²=？（x+y）²-4（x+y-1）=？

Answer 1

几道题都是利用完全平方公式 a²+2ab+b² = (a+b)² 进行分解:

4xy²-4x²y-y³
= -y(4x²-4xy+y²)
= -y(2x-y)²

3x³-18x²+27x
= 3x(x²-6x+9)
= 3x(x-3)²

(a-b)²-12(a-b)c+36c²
= (a-b+6c)²

(x+y)²-4(x+y-1)
= (x+y)²-4(x+y)+4
= (x+y+2)²

Answer 2

4xy²-4x²y-y³
=y(4xy-4x²-y²)
=-y[(2x)²-2*2x*y+y²]
=-y(2x-y)²

3x³-18x²+27x
=3x(x²-6x+9)
=3x(x-3)²

(a-b)²-12(a-b)c+36c²
=(a-b-6c)²

(x+y)²-4(x+y-1)
=(x+y)²-4(x+y)+4
=(x+y-2)²

Answer 3

y(4xy-4x^2-y^2)=-y(2x-y)^2
3x(x^2-6x+9)=3x(x-3)^2
[(a-b)-6c]^2=(a-b-6c)^2
（x+y）²-4（x+y)+4=(x+y+2)^2