-(-3x+5y)²+(3x+5y)²有没有简便方法

来源:学生作业帮助网 编辑:作业帮 时间:2024/06/21 06:00:37

-(-3x+5y)²+(3x+5y)²
有没有简便方法

-(-3x+5y)²+(3x+5y)²
=-9x^2+30xy-25y^2+9x^2+30xy+25y^2
=60xy

=(3x+5y)^2-(5y-3x)^2
=(3x+5y+5y-3x)(3x-5y-5y+3x)
=10y*6x
=60xy

令3x=a 5y=b
-(b-a)^2+(a+b)^2
=-b^2+2ab-a^2+a^2+2ab+b^2
=4ab
=60xy

(3x+5y)^2=9x^2+30xy+25y^2,(-3x+5y)^2=9x^2-30xy+25y^2,所以-(-3x+5y)²+(3x+5y)²=60xy