Question

Answer 1

a: \(a^2+b^2=\left(a+b\right)^2-2ab=3^2-2\cdot\left(-4\right)=9+8=17\)

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

\(=3^3-3\cdot3\cdot\left(-4\right)\)

=27+36

=63

c: \(a^5+b^5\)

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

\(=17\cdot63-\left(-4\right)^2\cdot3=1023\)