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Simplifying Algebraic Expressions: (2x + 3y)⁴ * (2x + 3y)⁵
This problem involves simplifying an expression with exponents and binomial multiplication. Let's break down the steps:
Understanding the Problem
We have the expression: (2x + 3y)⁴ * (2x + 3y)⁵
The goal is to simplify this expression to a more manageable form.
Applying the Rules of Exponents
One key rule of exponents states that when multiplying powers with the same base, we add the exponents.
Applying this to our problem:
(2x + 3y)⁴ * (2x + 3y)⁵ = (2x + 3y)⁽⁴⁺⁵⁾ = (2x + 3y)⁹
Simplifying Further (Optional)
While the expression (2x + 3y)⁹ is simplified, it can be expanded further using the binomial theorem or by repeated multiplication. This process is generally more tedious and may not be necessary for most applications.
Summary
We successfully simplified the expression (2x + 3y)⁴ * (2x + 3y)⁵ to (2x + 3y)⁹ by applying the rule of exponents for multiplying powers with the same base. Further simplification is possible by expanding the expression, but it may not always be necessary.