Question

Answer 1

a: \(x^2+y^2=\left(x+y\right)^2-2xy=a^2-2b\)

b: \(=\left(x+y\right)^3-3xy\left(x+y\right)\)

\(=a^3-3ab\)

Answer 2

\(x^2+y^2=x^2+2xy+y^2-2xy=\left(x+y\right)^2-2xy\)

=> \(x^2+y^2=a^2-2b\)

\(x^3+y^3=x^3+3x^2y+3xy^2+y^3-3x^2y-3xy^2\)

              \(=\left(x+y\right)^3-3xy\left(x+y\right)\)

=> \(x^3+y^3=a^3-3ab\)