Final answer:
To simplify (6x^2 - 3 + 5x^3) - (4x^3-2x^2 - 16), distribute the negative sign, group like terms, and combine them to get the simplified expression x^3 + 8x^2 + 13.
Step-by-step explanation:
To simplify the expression (6x^2 - 3 + 5x^3) - (4x^3 - 2x^2 - 16), you should combine like terms by subtracting the second set of parentheses from the first. Here are the steps you would take:
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- First, distribute the negative sign to each term inside the second parentheses: (6x^2 - 3 + 5x^3) - 4x^3 + 2x^2 + 16.
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- Next, rearrange the terms to group like terms together: 5x^3 - 4x^3 + 6x^2 + 2x^2 - 3 + 16.
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- Combine like terms: (5x^3 - 4x^3) + (6x^2 + 2x^2) + (-3 + 16).
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- Simplify the expression by performing the operations: x^3 + 8x^2 + 13.
This gives us the simplified expression: x^3 + 8x^2 + 13.