若(x-3y)²=(x+3y)²+M,M=?

若(x-3y)²=(x+3y)²+M,M=?
若(x-3y)²=(x+3y)²+M,M=?

若(x-3y)²=(x+3y)²+M,M=?
展开后可得.12Xy.是否求常数?

(x-3y)^2=x^2-6xy+9y^2
(x+3y)^2=x^2+6xy+9y^2
所以M=-12xy

解:M=(x-3y)²-(x+3y)²
=x^2-6xy+9y^2-(x^2+6xy+9y^2)
=x^2-6xy+9y^2-x^2-6xy-9y^2
=-12xy

若(x-3y)²=(x+3y)²+M,M= - 6xy