The first step in simplifying the expression \((2x^3 - 12x^2 + 5x - 3) - (7x^3 + 10x^2 - 3x + 20)\) is to distribute the negative sign in front of the second set of parentheses to each term inside of it. This will help eliminate the parentheses and rearrange the terms for easier combination.
So, distribute the negative sign:
\[ (2x^3 - 12x^2 + 5x - 3) - (7x^3 + 10x^2 - 3x + 20) = 2x^3 - 12x^2 + 5x - 3 - 7x^3 - 10x^2 + 3x - 20 \]
After this step, the expression reads:
\[ 2x^3 - 7x^3 - 12x^2 - 10x^2 + 5x + 3x - 3 - 20 \]
Next, you can combine like terms. But the first step is the distribution as shown above.
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