Answer
$7x^4+2x^3+4$
Work Step by Step
$(7x^4+3x^3-5x+1)-(x^3+8x^2-5x-3)\longrightarrow$ use the distributive property to multiply by -1
=$(7x^4+3x^3-5x+1)+(-x^3-8x^2+5x+3)\longrightarrow$ use the associative property to reorder
=$7x^4+(3x^3-x^3)+(-5x+5x)+(1+3)\longrightarrow$ combine like terms
=$7x^4+2x^3+4$
