完全平方公式题

来源：百度知道 编辑：UC知道 时间：2024/05/22 15:32:46
注:括号后的数为次方

(A+B-C)2

(X-Y-Z)2

(3X+2Y-4)(3X+2Y+4)

(3X+2Y+4)(3X-2Y-4)

[(X+3Y)(X-3Y)]2

1、(A+B-C)2=[(A+B)-C]2=(A+B)2-2(A+B)C+C2
2、(X-Y-Z)2=[(X-Y)2-2(X-Y)Z+Z2]
3、(3X+2Y-4)(3X+2Y+4)=(3X+2Y)2-16
4、(3X+2Y+4)(3X-2Y-4)=[3X+(2Y+4)][3X-(2Y+4)]=3=9X2-(2Y+4)2
5、[(X+3Y)(X-3Y)]2=(X2-9Y2)2=X4-18X2Y2+81Y4

(A+B-C)2
=A^2+B^2+C^2+2AB-2AC-2BC

(X-Y-Z)2
=X^2+Y^2+Z^2-2XY-2XZ-2YZ

(3X+2Y-4)(3X+2Y+4)
=(3X+2Y)^2-4^2
=9X^2+12XY+4Y^2-16

(3X+2Y+4)(3X-2Y-4)
=[3X+(2Y+4)][3X-(2Y+4)]
=(3X)^2-(2Y+4)^2
=9X^2-4Y^2-16Y-16

[(X+3Y)(X-3Y)]2
=[X^2-9Y^2]^2
=X^4-18X^2Y^2+81Y^4