Simplifying Algebraic Expressions: (a³  2a²)  (3a²  4a³)
This article will guide you through the process of simplifying the algebraic expression **(a³  2a²)  (3a²  4a³) **.
Understanding the Expression
The expression contains terms with variables raised to different powers. Here's a breakdown:
 a³: a variable 'a' raised to the power of 3 (a * a * a)
 a²: a variable 'a' raised to the power of 2 (a * a)
To simplify, we need to combine like terms. Like terms are terms that have the same variable and the same exponent.
Simplifying the Expression

Distribute the negative sign: The minus sign in front of the second set of parentheses means we need to multiply each term inside by 1: (a³  2a²) + (1 * 3a²) + (1 * 4a³)

Combine like terms: Identify terms with the same variable and exponent: a³ + 4a³  2a²  3a²

Simplify: Combine the coefficients of the like terms: 5a³  5a²
The Final Answer
The simplified form of the expression (a³  2a²)  (3a²  4a³) is 5a³  5a².