Expanding and Simplifying Algebraic Expressions
In this article, we will explore the process of expanding and simplifying algebraic expressions, using the example of (-x^3 + 2x - 4) - (x^3 + 2x^2 - 5x + 3)
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Step 1: Expand the Expression
To expand the expression, we need to follow the order of operations (PEMDAS):
- Distribute the negative sign to the terms inside the second parentheses:
(-x^3 + 2x - 4) - (x^3 + 2x^2 - 5x + 3) = -x^3 + 2x - 4 - x^3 - 2x^2 + 5x - 3
Step 2: Combine Like Terms
Combine like terms:
-x^3 + 2x - 4 - x^3 - 2x^2 + 5x - 3 = -2x^3 - 2x^2 + 7x - 7
Simplified Expression
The simplified expression is:
-2x^3 - 2x^2 + 7x - 7
In conclusion, we have successfully expanded and simplified the algebraic expression (-x^3 + 2x - 4) - (x^3 + 2x^2 - 5x + 3)
to obtain the final result -2x^3 - 2x^2 + 7x - 7
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