Question

If $x♠y=(x+y{)}^2$ for all positive integers, what is the value of $\left(1♠2\right)♠3$?

Answer 1

We are given that $x♠y=(x+y{)}^2$.

To find $\left(1♠2\right)♠3$, let us first find $1♠2$ by substituting $x=1$ and $y=2$ in $x♠y=(x+y{)}^2$ as shown below:

$1♠2=(1+2{)}^2=3^2=9$

Now, we find $\left(1♠2\right)♠3$, that is $9♠3$:

$9♠3=(9+3{)}^2={12}^2=144$

Hence, $\left(1♠2\right)♠3=144$.