(2x2y)(3xy)3.jpeg "(4xy)(2x2y)(3xy)3")
Simplifying Algebraic Expressions: (4xy)(2x²y)(3xy)³
This article will guide you through simplifying the algebraic expression (4xy)(2x²y)(3xy)³.
Understanding the Expression
The expression involves the product of multiple terms with variables and exponents. Let's break it down:
- (4xy): This term represents the product of 4, x, and y.
- (2x²y): This term represents the product of 2, x squared, and y.
- (3xy)³: This term represents the cube of the product of 3, x, and y.
Simplifying the Expression
To simplify the expression, we can follow these steps:
- Expand the Cube: (3xy)³ is the same as (3xy)(3xy)(3xy)
- Combine Coefficients: Multiply the numerical coefficients together: 4 * 2 * 3 * 3 * 3 = 216.
- Combine Variables: Multiply the variables together, adding their exponents: x * x² * x * x * x = x⁶ and y * y * y * y = y⁴.
Final Result
After combining the coefficients and variables, we arrive at the simplified expression: 216x⁶y⁴.
Key Concepts
- Exponents: x² means x multiplied by itself twice (x * x).
- Order of Operations: Remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions.
- Multiplication of Variables: When multiplying variables with exponents, add their exponents.
Conclusion
By applying the rules of exponents and multiplication, we were able to simplify the complex algebraic expression (4xy)(2x²y)(3xy)³ into the much simpler form 216x⁶y⁴.