(a^3-2a^2)-(3a^2-4a^3)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (a^3 - 2a^2) - (3a^2 - 4a^3)

This article will guide you through simplifying the algebraic expression: (a^3 - 2a^2) - (3a^2 - 4a^3). We will use the principles of combining like terms to achieve a simplified result.

Understanding the Steps

1. Distribute the negative sign: The minus sign in front of the second set of parentheses means we multiply each term inside the parentheses by -1.

   (a^3 - 2a^2) + (-1 * 3a^2) + (-1 * -4a^3)

2. Simplify: Multiplying by -1 simply changes the sign of each term.

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

3. Combine like terms: Identify terms with the same variable and exponent. Combine their coefficients.

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

4. Final simplification: Perform the addition and subtraction of coefficients.

   5a^3 - 5a^2

Conclusion

Therefore, the simplified form of the expression (a^3 - 2a^2) - (3a^2 - 4a^3) is 5a^3 - 5a^2.