Question

Answer 1

e: \(E=2\left(x^3+y^3\right)-3\left(x^2+y^2\right)\)

\(=2\left\lbrack\left(x+y\right)^3-3xy\left(x+y\right)\right\rbrack-3\left\lbrack\left(x+y\right)^2-2xy\right\rbrack\)

\(=2\left\lbrack1-3xy\right\rbrack-3\left(1-2xy\right)=2-6xy-3+6xy=2-3=-1\)

f: \(F=x^3+y^3+3xy\)

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

=1-3xy+3xy

=1

g: \(G=x^3-y^3-3xy\)

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

=1+3xy-3xy

=1