Question

rut gon bieu thuc :

a,\(\left(a+b\right)^3-\left(a-b\right)^3-6a^2b\)

b,\(\left(a+b\right)^3+\left(a-b\right)^3-6ab^2\)

Answer 1

a) \(\left(a+b\right)^3-\left(a-b\right)^3-6a^2b\)

\(\Leftrightarrow a^3+3a^2b+3ab^2+b^3-\left(a^3-3a^2b+3ab^2-b^3\right)-6a^2b\)

\(\Leftrightarrow a^3+3a^2b+3ab^2+b^3-a^3+3a^2b-3ab^2+b^3-6a^2b\)

\(\Leftrightarrow2b^3\)

b) \(\left(a+b\right)^3-\left(a-b\right)^3-6ab^2\)

\(\Leftrightarrow a^3+3a^2b+3ab^2+b^3-\left(a^3-3a^2b+3ab^2-b^3\right)-6ab^2\)

\(\Leftrightarrow a^3+3a^2b+3ab^2+b^3-a^3+3a^2b-3ab^2+b^3-6ab^2\)

\(\Leftrightarrow2b^3+6a^2b-6ab^2\)