Question

chứng minh (a+b)^3=a^3+b^3+3*a*b*(a*b) cho biết a*b=2; a+b=-3. tính a^3+b^3

Answer 1

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

\(=a^3+b^3+3ab\left(a+b\right)\)

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

\(=\left(-3\right)^3-3\cdot2\cdot\left(-3\right)\)

=27+9x2=45

Answer 2

\(\left(a+b\right)^3=a^3+b^3+3ab\left(a+b\right)\)

\(\Leftrightarrow\left(-3\right)^3=a^3+b^3+3.2.\left(-3\right)\)

\(\Leftrightarrow-27=a^3+b^3-18\)

\(\Leftrightarrow a^3+b^3=-9\)