作业帮(m-2n)^2+(3m-n)(2m+2n)-(2m+n)(2m-n) 已知m+n=4 mn=1
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/28 20:13:11
(m-2n)^2+(3m-n)(2m+2n)-(2m+n)(2m-n) 已知m+n=4 mn=1
(m-2n)^2+(3m-n)(2m+2n)-(2m+n)(2m-n) 已知m+n=4 mn=1
(m-2n)^2+(3m-n)(2m+2n)-(2m+n)(2m-n) 已知m+n=4 mn=1
(m-2n)^2+(3m-n)(2m+2n)-(2m+n)(2m-n)
=m²-4mn+4n²+6m²+4mn-2n²-4m²+n²
=3m²+3n²
=3(m²+n²)
=3[(m+n)²-2mn]
=3×(16-2)
=3×14
=42
(m-2n)^2+(3m-n)(2m+2n)-(2m+n)(2m-n)
=m^2-4mn+4n^2+6m^2+4mn-2n^2-4m^2+n^2
=3m^2+3n^2
=3(m^2+n^2)
=3{(m+n)^2-2mn}
=3(4^2-2x1)
=42
求值：(m-2n)²+(3m-n)(2m+2n)-(2m+n)(2m-n) 已知m+n=4 mn=1
(m-2n)²+(3m-n)(2m+2n)-(2m+n)(2m-n) =(m²-4mn+4n²)+(6m²+4mn-2n²)-(4m²-n²)
=3m²+3n²=3(m²+n²)=3[(m+n)²-2mn]=3(16-2)=42.
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