$\text{P = A + B.}$
$\text{= ($5x^2$ - 3xy + $7y^2$) + ($6x^2$ - 8xy + $9y^2$).}$
$\text{= $5x^2$ - 3xy + $7y^2$ + $6x^2$ - 8xy + $9y^2$.}$
$\text{= ($5x^2$ + $6x^2$) + ($7y^2$ + $9y^2$) + (- 3xy - 8xy).}$
$\text{= $11x^2$ + $16y^2$ - 11xy.}$
$\text{Q = A - B.}$
$\text{= ($5x^2$ - 3xy + $7y^2$) - ($6x^2$ - 8xy + $9y^2$).}$
$\text{= $5x^2$ - 3xy + $7y^2$ - $6x^2$ + 8xy - $9y^2$.}$
$\text{= ($5x^2$ - $6x^2$) + ($7y^2$ - $9y^2$) + (- 3xy + 8xy).}$
$\text{= $-x^2$ - $2y^2$ + 5xy.}$
