ANSWER
[tex]P-G = 11{w}^{4} - 5 {w}^{2} {z}^{2} - 4z^{4}[/tex]
EXPLANATION
The given polynomials are:
[tex]G = - 3 {w}^{4} + 2 {w}^{2} {z}^{2} + 5z^{4} [/tex]
and
[tex]P = 8 {w}^{4} - 3{w}^{2} {z}^{2} + z^{4} [/tex]
We want to subtract these two polynomials.
[tex]P-G = 8 {w}^{4} - 3{w}^{2} {z}^{2} + z^{4} - (- 3 {w}^{4} + 2 {w}^{2} {z}^{2} + 5z^{4} )[/tex]
Expand the right hand side to obtain:
[tex]P-G = 8 {w}^{4} - 3{w}^{2} {z}^{2} + z^{4} + 3 {w}^{4} - 2 {w}^{2} {z}^{2} - 5z^{4} [/tex]
Group the similar terms:
[tex]P-G = 8 {w}^{4} + 3 {w}^{4}- 3{w}^{2} {z}^{2} - 2 {w}^{2} {z}^{2} - 5z^{4} + z^{4}[/tex]
Combine the similar terms to get:
[tex]P-G = 11{w}^{4} - 5 {w}^{2} {z}^{2} - 4z^{4}[/tex]
