Can I express $x^7y+xy+x+1$ by a repeated use of operation $xy+x+y+1$?

Question

A certain calculator can only give the result of $xy+x+y+1$ for any two real numbers $x$ and $y$.

How to use this calculator to calculate $x^7y+xy+x+1$ for any given $x$ and $y$?

When $x$ and $y$ are equal, it will give $(x+1)^2$. But I cannot proceed beyond that.

Answer 1

Give $x^7$ and $y$ to the calculator, to get $R_1 = x^7y + x^7+y +1$.
Give $x$ and $y$ to the calculator, to get $R_2 = xy+x+y+1$.
Add $R_1$ and $R_2$ to get, $R = R_1+R_2 = x^7y + x^7 + x+xy + 2y+1$.
Subtract $x^7$ and $2y$ from $R$ to get the required.

Answer 2

Follow these steps:

1. Give $(x,x)$ to the calculator to get $x^2 + 2x + 1$ and subtract $2x + 1$ from this. You can even get $2x$ from the calculator by giving in $(x,1)$ to get $2x + 2$.
2. Now, using prev result, give $(x^2, x^2)$ to get $x^4+ 2x^2 + 1$. Use previous result to obtain $x^4$.
3. Using previous result, give $(x^4, x^2)$ to get $x^6 + x^4 + x^2 + 1$. Subtract values to get $x^6$.
4. Give $(x^6, x)$ to get $x^7 + x^6 + x + 1$ and from this extract $x^7$.
5. Give $(x^7, y)$ to get $x^7y + x^7 + y + 1$. From this pull out the $x^7y$ to get $x^7y$
6. Give $(x,y)$ to get $xy + x + y + 1$. From this pull out the $y$ to get $xy + x + 1$
7. Add 5. and 6. to get $x^7y + xy + x + 1$.

This question makes little sense. Are there more stringent rules on what you aren't allowed to do?