Simplifying Polynomial Expressions
This article will guide you through the process of simplifying the polynomial expression: (5x^3 - x + 2x^2) + (7 - 4x) - (6x^2 + 5x^3 - 3)
Understanding the Steps
To simplify this expression, we will follow these steps:
- Remove parentheses: We will distribute any negative signs in front of parentheses.
- Combine like terms: We will group together terms with the same variable and exponent.
- Simplify: We will perform the necessary arithmetic operations.
Simplifying the Expression
Let's break down the simplification process step by step:
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Removing parentheses:
- The first set of parentheses doesn't have a negative sign in front, so we can simply remove them.
- The second set of parentheses also doesn't have a negative sign in front.
- The third set of parentheses has a negative sign in front. We distribute this negative sign to each term inside the parentheses:
- -(6x^2 + 5x^3 - 3) = -6x^2 - 5x^3 + 3
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Combining like terms:
- x^3 terms: 5x^3 - 5x^3 = 0x^3 (these terms cancel out)
- x^2 terms: 2x^2 - 6x^2 = -4x^2
- x terms: -x - 4x = -5x
- Constant terms: 7 + 3 = 10
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Simplifying:
Putting all the simplified terms together, we get:
0x^3 - 4x^2 - 5x + 10
Final Answer
Therefore, the simplified form of the given polynomial expression is -4x^2 - 5x + 10.