-(-8a%5E2%2Ba-7a%5E4).jpeg "(-7a^4-a+4a^2)-(-8a^2+a-7a^4)")
Simplifying Algebraic Expressions: (-7a^4 - a + 4a^2) - (-8a^2 + a - 7a^4)
This article will guide you through the process of simplifying the algebraic expression: (-7a^4 - a + 4a^2) - (-8a^2 + a - 7a^4).
Understanding the Expression
The expression involves:
- Variables: 'a' represents a variable, and its powers (a^4, a^2) represent different exponents.
- Coefficients: Numbers multiplying the variables (e.g., -7, -1, 4, -8, 1, -7).
- Parentheses: Indicate grouping and order of operations.
Simplifying the Expression
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Distribute the negative sign: The minus sign before the second set of parentheses indicates that we need to change the signs of all the terms inside the parentheses.
(-7a^4 - a + 4a^2) + 8a^2 - a + 7a^4 -
Combine like terms: Combine terms with the same variable and exponent.
- a^4 terms: -7a^4 + 7a^4 = 0
- a^2 terms: 4a^2 + 8a^2 = 12a^2
- a terms: -a - a = -2a
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Write the simplified expression: The simplified form of the expression is:
12a^2 - 2a
Conclusion
By following the steps of distributing the negative sign and combining like terms, we have successfully simplified the expression (-7a^4 - a + 4a^2) - (-8a^2 + a - 7a^4) to 12a^2 - 2a. This simplified form is easier to work with and understand.