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(3ab^2)(a^2c^5)

2 min read Jun 16, 2024
(3ab^2)(a^2c^5)

Simplifying Algebraic Expressions: (3ab^2)(a^2c^5)

This article will guide you through the process of simplifying the algebraic expression (3ab^2)(a^2c^5).

Understanding the Basics

To simplify this expression, we need to understand the following concepts:

  • Coefficients: The numerical part of a term, like 3 in our expression.
  • Variables: Symbols representing unknown values, like a, b, and c.
  • Exponents: Indicate how many times a variable is multiplied by itself. For example, b^2 represents b * b.

Applying the Rules

  1. Multiply the coefficients:

    • The coefficients are 3 and 1 (since a^2c^5 has an implied coefficient of 1).
    • 3 * 1 = 3

  2. Multiply the variables with the same base:

    • a * a^2 = a^(1+2) = a^3
    • b^2 * (no b term) = b^2
    • (no c term) * c^5 = c^5

  3. Combine the results:

    • 3 * a^3 * b^2 * c^5 = 3a^3b^2c^5

The Simplified Expression

Therefore, the simplified form of (3ab^2)(a^2c^5) is 3a^3b^2c^5.

Key Takeaways

  • When multiplying terms with the same base, add their exponents.
  • Coefficients are multiplied together.
  • Variables with different bases remain separate.

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