To simplify the expression \((2x^3 - 12x^2 + 5x - 3) - (7x^3 + 10x^2 - 3x + 20)\), the first step is to distribute the negative sign across the second polynomial. This means you will subtract each term in the second polynomial from the corresponding term in the first polynomial.
Here are the steps:
- Write down the first polynomial: \(2x^3 - 12x^2 + 5x - 3\).
- Distribute the negative sign to the second polynomial: \[ -(7x^3 + 10x^2 - 3x + 20) = -7x^3 - 10x^2 + 3x - 20. \]
- Now, combine both expressions: \[ (2x^3 - 12x^2 + 5x - 3) + (-7x^3 - 10x^2 + 3x - 20). \]
Now you can proceed to combine like terms.
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