Đáp án:
Giải thích các bước giải:
`(\frac{m+n}{2})^3-(\frac{m-n}{2})^3`
`=(\frac{m+n}{2}-\frac{m-n}{2})[(\frac{m+n}{2})^2+\frac{m+n}{2}.\frac{m-n}{2}+(\frac{m-n}{2})^2]`
`=\frac{m+n-m+n}{2}(\frac{m^2+2mn+n^2}{4}+\frac{m^2-n^2}{4}+\frac{m^2-2mn+n^2}{4})`
`=n.\frac{m^2+2mn+n^2+m^2-n^2+m^2-2mn+n^2}{4}`
`=\frac{n(3m^2+n^2)}{4}`
`=\frac{3m^2n+n^3}{4} (đpcm)`