To simplify the expression \((3^{2x} + 3)(3^{3x} - 2)\), we can expand it using the distributive property (also known as the FOIL method for binomials):

\[
(3^{2x} + 3)(3^{3x} - 2)
\]

Expanding this:

1. Multiply the first terms:  
   \[3^{2x} \times 3^{3x} = 3^{2x + 3x} = 3^{5x}\]

2. Multiply the outer terms:  
   \[3^{2x} \times -2 = -2 \times 3^{2x}\]

3. Multiply the inner terms:  
   \[3 \times 3^{3x} = 3^{1+3x} = 3^{3x + 1}\]

4. Multiply the last terms:  
   \[3 \times -2 = -6\]

Putting it all together:

\[
3^{5x} - 2 \times 3^{2x} + 3^{3x+1} - 6
\]

So, the expanded expression is:

\[
3^{5x} - 2 \times 3^{2x} + 3^{3x+1} - 6
\]

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you simplify expressions involving exponents with the same base?
2. What is the distributive property in algebra?
3. How do you factor expressions like \(3^{5x} - 2 \times 3^{2x}\)?
4. What is the difference between expanding and factoring an expression?
5. How do you solve equations involving exponential expressions?

**Tip:** When working with exponents, remember that multiplying terms with the same base involves adding the exponents.

Learn how to simplify the expression (3^(2x) + 3)(3^(3x) - 2) using the distributive property. This problem involves exponents and algebraic manipulation, suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation