Question

把下列各式因式分解。x﹙x＋4﹚＋4. 2mx²－4mxy＋2my². ¼x＋x³－x².

x³y＋2x²y²＋xy³.

Answer 1

x﹙x＋4﹚＋4
=x²+4x+4
=(x+2)²

2mx²－4mxy＋2my². ¼x＋x³－x².
=2m(x²-2xy+y²)
=2m（x-y）²

¼x＋x³－x².
=x(¼-x＋x² )
=x(x-1/2)²

x³y＋2x²y²＋xy³.
=xy(x²+2xy+y²)
=xy(x+y)²

Answer 2

解：x﹙x＋4﹚＋4=x^2+4x+4=(x+2)^2
2mx²－4mxy＋2my²=2m(x²－2xy＋y²)=2m(x-y)²
¼x＋x³－x²=¼x(1＋4x²-4x)=¼x(2x-1)²
x³y＋2x²y²＋xy³=xy(x²+2xy+y²)=xy(x+y)²