计算:(2m+3n-p)²-(2m-3n+p)²

计算:(2m+3n-p)²-(2m-3n+p)²
计算:(2m+3n-p)²-(2m-3n+p)²

计算:(2m+3n-p)²-(2m-3n+p)²
=（2m+3n-p+2m-3n+p）（2m+3n-p-2m+3n-p）
=4m（6n-2p）
=24mn-8p

相当于公式：A²-B²=（A+B）*（A-B）

原式=(2m+3n-p+2m-3n+p)*(2m+3n-p-2m+3n-p)=24mn-8mp，用平方差公式：a^2-b^2=(a+b)*(a-b)

=[(2m+3n-p)+(2m-3n+p)]*[(2m+3n-p)-(2m-3n+p)]
=4m(6n-2p)
=24mn-8p