`a)` P($x$) + Q($x$) + R($x$) = (-$5x^3$ + $7x^2$ - $x$ + $8$) + ($4x^3$ - $7x$ + $3$) + ($6x^3$ + $4x$)

= -$5x^3$ + $7x^2$ - $x$ + $8$ + $4x^3$ - $7x$ + $3$ + $6x^3$ + $4x$

= (-$5x^3$ + $4x^3$ + $6x^3$) + $7x^2$ +  (- $x$ - $7x$ + $4x$) + $8$

= $5x^3$ + $7x^2$ + (-$4x$) + $12$

`b)` P($x$) - Q($x$) + R($x$) = (-$5x^3$ + $7x^2$ - $x$ + $8$) - ($4x^3$ - $7x$ + $3$) + ($6x^3$ + $4x$)

= -$5x^3$ + $7x^2$ - $x$ + $8$ - $4x^3$ + $7x$ - $3$ + $6x^3$ + $4x$

= (-$5x^3$ - $4x^3$ + $6x^3$) + $7x^2$ + (-$x$ + $7x$ + $4x$) + $8$

= -$3x^3$ + $7x^2$ + $10x$ + $8$

$#yameyane$

`color{<white>}{\text{@Kudo Shinichi}}`