Simplifying Algebraic Expressions: (a^3  2a^2)  (3a^2  4a^3)
This article will guide you through the process of simplifying the algebraic expression (a^3  2a^2)  (3a^2  4a^3).
Understanding the Steps
To simplify this expression, we will follow these steps:

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

Combine like terms: Identify terms with the same variable and exponent, and combine their coefficients.
Simplifying the Expression
Step 1: Distribute the negative sign.
(a^3  2a^2) *1(3a^2  4a^3) = a^3  2a^2  3a^2 + 4a^3
Step 2: Combine like terms.
a^3 + 4a^3  2a^2  3a^2 = 5a^3  5a^2
Conclusion
The simplified form of the expression (a^3  2a^2)  (3a^2  4a^3) is 5a^3  5a^2.
By following these steps, you can effectively simplify algebraic expressions and express them in their most concise form.