First we have to find the sum of (x2 + 3y2 – 6xy), (2x2 – y2 + 8xy), (y2 + 8) and (x2 – 3xy)
={(x2 + 3y2 – 6xy) + (2x2 – y2 + 8xy) + ( y2 + 8) + (x2 – 3xy)}
={x2 + 3y2 – 6xy + 2x2 – y2 + 8xy + y2 + 8 + x2 – 3xy}
= {x2+ 2x2+ x2 + 3y2– y2 + y2– 6xy + 8xy – 3xy + 8}
= 4x2 + 3y2 – xy + 8
Now, from the result subtract the −3x2 + 4y2 – xy + x – y + 3
Therefore, required expression = (4x2 + 3y2 – xy + 8) – (- 3x2 + 4y2 – xy + x – y + 3)
= 4x2 + 3y2 – xy + 8 + 3x2 – 4y2 + xy – x + y – 3
= 4x2 + 3x2+ 3y2– 4y2– x + y – 3 + 8
= 7x2 – y2– x + y + 5.