$4{n}^{4}-8n+4-\left( 8{n}^{2}+4{n}^{4}+1 \right)$
When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses$4{n}^{4}-8n+4-8{n}^{2}-4{n}^{4}-1$
Since two opposites add up to $0$, remove them from the expression$-8n+4-8{n}^{2}-1$
Subtract the numbers$-8n+3-8{n}^{2}$
Use the commutative property to reorder the terms$-8{n}^{2}-8n+3$