Final answer:
To simplify the given expression, like terms are combined to result in 8x^3+2x^2-3x+4 after adding the coefficients of identical powers of x.
Step-by-step explanation:
To simplify the expression (7x^3+7x^2-4)+(x^3-5x^2-3x+8), we need to combine like terms. The terms that are like each other have the same variable to the same power.
Step 1: Identify like terms in both polynomials - $7x^3$ and $x^3$, $7x^2$ and $-5x^2$, $-3x$ (there is no like term to combine with this in the first polynomial), $-4$ and $8$.
Step 2: Combine the like terms - Add the coefficients of $x^3$ terms, the $x^2$ terms and the constant terms separately.
Step 3: Therefore, (7x^3+7x^2-4)+(x^3-5x^2-3x+8) simplifies to 8x^3+2x^2-3x+4.
Finally, check that the simplified form is reasonable by confirming all like terms have been correctly combined and no terms are missing.