Try rewriting the expression by distributing the negative sign to every term in the second parentheses, then drop the parentheses entirely.

After rewriting, group $x^3$ terms together, $x^2$ terms together, $x$ terms together, and constants together. Then combine the coefficients in each group, paying close attention to plus and minus signs.

In Desmos, type the original expression as one line, for example: (5x^3 - 2x^2 + x - 3) - (2x^3 + x^2 - 4x + 5) and press Enter. This creates a graph for the original polynomial.

For each option, type a new expression of the form choice - ((5x^3 - 2x^2 + x - 3) - (2x^3 + x^2 - 4x + 5)). For example, for option A, type 3x^3 - 3x^2 - 3x - 8 - ((5x^3 - 2x^2 + x - 3) - (2x^3 + x^2 - 4x + 5)).

Look at the graphs or the expression values: the correct choice will give an expression that simplifies to 0 for all $x$ (its graph will be the horizontal line $y = 0$). That option is equivalent to the original expression.

The expression is

Subtracting a polynomial means you subtract each term in the second parentheses. A quick way to do this is to think of multiplying the entire second parentheses by $-1$ (distribute the minus sign).

Distribute the minus sign to each term in the second set of parentheses:

• $-(2x^3) = -2x^3$
• $-(x^2) = -x^2$
• $-(-4x) = +4x$
• $-(5) = -5$

So the whole expression becomes

Now group terms with the same power of $x$:

• $x^3$ terms: $5x^3$ and $-2x^3$
• $x^2$ terms: $-2x^2$ and $-x^2$
• $x$ terms: $x$ and $4x$
• Constant terms: $-3$ and $-5$

Combine each group:

• $5x^3 - 2x^3 = 3x^3$
• $-2x^2 - x^2 = -3x^2$
• $x + 4x = 5x$
• $-3 - 5 = -8$

Putting all the combined terms together, the simplified expression is

This matches answer choice B) $3x^3 - 3x^2 + 5x - 8$.