Calculate: (4n^4-8n+4)-(8n^2+4n^4+1)

Expression: $\left( 4{n}^{4}-8n+4 \right)-\left( 8{n}^{2}+4{n}^{4}+1 \right)$

Remove unnecessary parentheses

$4{n}^{4}-8n+4-\left( 8{n}^{2}+4{n}^{4}+1 \right)$

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

$-8{n}^{2}-8n+3$