(-3a^3+2a^2-4)+(a^3-3a^2-5a+7)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the following polynomial expression:

(-3a^3 + 2a^2 - 4) + (a^3 - 3a^2 - 5a + 7)

Understanding the Problem

The expression involves two sets of parentheses containing polynomial terms. Our goal is to combine like terms to arrive at a simplified expression.

Steps for Simplification

1. Remove the Parentheses: Since we are adding the two sets of polynomials, the parentheses simply serve as grouping symbols and can be removed.

2. Identify Like Terms: Like terms have the same variable and exponent. In our expression, the like terms are:

   • a^3 terms: -3a^3 and a^3
   • a^2 terms: 2a^2 and -3a^2
   • a terms: -5a (only one term)
   • Constant terms: -4 and 7

3. Combine Like Terms: Add the coefficients of the like terms:

   • a^3 terms: -3a^3 + a^3 = -2a^3
   • a^2 terms: 2a^2 - 3a^2 = -a^2
   • a terms: -5a (remains unchanged)
   • Constant terms: -4 + 7 = 3

4. Write the Simplified Expression: Combining the simplified terms, we get:

   -2a^3 - a^2 - 5a + 3

Conclusion

Therefore, the simplified form of the expression (-3a^3 + 2a^2 - 4) + (a^3 - 3a^2 - 5a + 7) is -2a^3 - a^2 - 5a + 3. This process demonstrates the fundamental steps involved in simplifying polynomial expressions, involving the identification and combination of like terms.