%2B(%E2%88%928w2%2Bw%2B3).jpeg "(−w3+8w2−3w)+(−8w2+w+3)")
Simplifying the Expression: (-w3 + 8w2 - 3w) + (-8w2 + w + 3)
This article will guide you through the steps of simplifying the given expression: (-w3 + 8w2 - 3w) + (-8w2 + w + 3).
Understanding the Expression
The expression consists of two sets of terms enclosed in parentheses. Let's break down each set:
- (-w3 + 8w2 - 3w): This set includes terms with different powers of 'w'.
- -w3: This represents the term with the highest power of 'w' (3).
- 8w2: This represents the term with the power of 'w' as 2.
- -3w: This represents the term with 'w' raised to the power 1.
- (-8w2 + w + 3): This set also includes terms with different powers of 'w', along with a constant term.
- -8w2: This represents the term with 'w' raised to the power 2.
- w: This represents the term with 'w' raised to the power 1.
- 3: This is a constant term.
Simplifying the Expression
To simplify the expression, we need to combine like terms. Like terms are those that have the same variable raised to the same power.
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Remove parentheses: Since we are adding the two sets of terms, we can remove the parentheses without changing the signs of the terms:
-w3 + 8w2 - 3w - 8w2 + w + 3
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Combine like terms:
- w3 terms: There is only one term with w3: -w3
- w2 terms: We have 8w2 and -8w2, which combine to give 0
- w terms: We have -3w and w, which combine to give -2w
- Constant terms: We have only one constant term: 3
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Write the simplified expression:
-w3 + 0 - 2w + 3
Therefore, the simplified form of the expression is -w3 - 2w + 3.
Conclusion
By combining like terms, we have successfully simplified the expression (-w3 + 8w2 - 3w) + (-8w2 + w + 3) to -w3 - 2w + 3. This process demonstrates how to handle expressions with multiple terms and different powers of variables.