-(5x%5E3%2B6x-3).jpeg "(5x-12x^2+9x^3)-(5x^3+6x-3)")
Simplifying the Expression: (5x-12x^2+9x^3)-(5x^3+6x-3)
This article will guide you through simplifying the given expression: (5x-12x^2+9x^3)-(5x^3+6x-3).
Understanding the Basics
Before we start, let's recall some key concepts:
- Combining Like Terms: We can only add or subtract terms that have the same variable and exponent. For example, 5x and 6x are like terms, but 5x and 5x² are not.
- Distributing the Negative Sign: When we have a minus sign in front of parentheses, it means we distribute the negative sign to each term inside the parentheses.
Step-by-Step Solution
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Distribute the negative sign:
(5x - 12x² + 9x³) - (5x³ + 6x - 3) becomes 5x - 12x² + 9x³ - 5x³ - 6x + 3
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Rearrange the terms by their exponents:
9x³ - 5x³ - 12x² + 5x - 6x + 3
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Combine like terms:
(9x³ - 5x³) + (-12x²) + (5x - 6x) + 3
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Simplify:
4x³ - 12x² - x + 3
Final Answer
The simplified expression is 4x³ - 12x² - x + 3.