Simplify x^4+3x^3-2x^3-5x^2-x+x^2+x+1+7x^4

$x^{4} + 3 x^{3} - 2 x^{3} - 5 x^{2} - x + x^{2} + x + 1 + 7 x^{4}$

Combine the opposite terms in $x^{4} + 3 x^{3} - 2 x^{3} - 5 x^{2} - x + x^{2} + x + 1 + 7 x^{4}$ .

Add $- x$ and $x$ .

$x^{4} + 3 x^{3} - 2 x^{3} - 5 x^{2} + x^{2} + 0 + 1 + 7 x^{4}$

Add $x^{4} + 3 x^{3} - 2 x^{3} - 5 x^{2} + x^{2}$ and $0$ .

$x^{4} + 3 x^{3} - 2 x^{3} - 5 x^{2} + x^{2} + 1 + 7 x^{4}$

Add $x^{4}$ and $7 x^{4}$ .

$8 x^{4} + 3 x^{3} - 2 x^{3} - 5 x^{2} + x^{2} + 1$

Subtract $2 x^{3}$ from $3 x^{3}$ .

$8 x^{4} + x^{3} - 5 x^{2} + x^{2} + 1$

Add $- 5 x^{2}$ and $x^{2}$ .

$8 x^{4} + x^{3} - 4 x^{2} + 1$