(4xy)(2xy)3.jpeg "(3xy2)(4xy)(2xy)3")
Simplifying Algebraic Expressions: (3xy²)(4xy)(2xy)³
This article will guide you through the process of simplifying the algebraic expression: (3xy²)(4xy)(2xy)³.
Understanding the Basics
Before diving into the simplification, let's refresh some key concepts:
- Coefficients: Numbers that multiply variables. In our expression, the coefficients are 3, 4, and 2.
- Variables: Letters representing unknown values. Here, the variables are x and y.
- Exponents: Small numbers written above and to the right of a variable, indicating how many times the variable is multiplied by itself.
- Order of Operations: We follow the PEMDAS/BODMAS rule: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Simplifying the Expression
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Simplify the exponent: (2xy)³ = (2xy)(2xy)(2xy) = 8x³y³
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Combine the coefficients: 3 * 4 * 8 = 96
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Multiply the variables: x * x * x³ = x⁵ and y² * y * y³ = y⁶
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Combine the results: 96x⁵y⁶
Final Result
Therefore, the simplified form of (3xy²)(4xy)(2xy)³ is 96x⁵y⁶.
Key Takeaways
- When multiplying variables with exponents, add their exponents.
- Simplify exponents first, followed by multiplication of coefficients and variables.
- Remember to follow the order of operations.
By following these steps, you can confidently simplify complex algebraic expressions.