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

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)

Simplify: Multiplying by 1 simply changes the sign of each term.
(a^3  2a^2)  3a^2 + 4a^3

Combine like terms: Identify terms with the same variable and exponent. Combine their coefficients.
(a^3 + 4a^3) + (2a^2  3a^2)

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.