a) \(\left(m+n\right)^2-\left(m-n\right)^2+\left(m+n\right)\left(m-n\right)\)

\(=\left(m+n+m-n\right)\left(m+n-m+n\right)+m^2-n^2\)

\(=m^2-n^2+4mn\)

b) \(\left(a+b\right)^3+\left(a-b\right)^3-2a^3\)

\(=\left(a+b-a+b\right)\left[\left(a+b\right)^2-\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]-2a^3\)

\(=2b\left[a^2+2ab+b^2-a^2+b^2+a^2-2ab+b^2\right]-2a^3\)

\(=2b\left(a^2+3b^2\right)-2a^3\)

\(=2a^2b+6b^3-2a^3.\)

Tương tự áp dụng các HĐT.