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When working with algebraic expressions, you often need to multiply different terms. This means multiplying coefficients (the numbers) and variables separately.
For example, in the problem given, you multiply 2m by each term inside the parentheses (3m and 2).
Using the distributive property, this looks like: \(2m(3m + 2) = 2m \times 3m + 2m \times 2\)
Next, let's multiply the terms one-by-one: \ 2m \times 3m = 6m^2 \ 2m \times 2 = 4m
Remember to first multiply the numbers (coefficients) and then the variables. Here: \2 \times 3 = 6\ and \(m \times m = m^2\). Finally, combine the results: \6m^2 + 4m.This multiplication step is crucial to simplify algebraic expressions.

An algebraic expression is a mathematical phrase that can include numbers, variables (like m or n), and operation symbols (like +, -, *, /).
In our exercise, we started with an expression: 2m(3m + 2).
By distributing 2m, we re-wrote the expression in a simpler form.
Algebraic expressions are powerful because they let you generalize mathematical problems.
When you simplify them, you make them easier to use in other calculations.
In this problem, once simplified, the expression helps understand how different terms relate to each other and how to break them down step by step. Remember:
Combining like terms helps in reducing the complexity of algebraic expressions.

Polynomials are a type of algebraic expression where terms are added together.
They can include constants, variables, and exponents (powers).
Our final expression, 6m^2 + 4m, is a polynomial. Here:
- 6m^2 is the quadratic term (since it has an exponent of 2).
- 4m is the linear term (since the variable has an exponent of 1).
- If there were any numbers without variables, they would be constant terms.
Polynomials can be classified by their degree (the highest exponent of the variable). Here it is 2 (since the highest term is m^2). Simplifying polynomials is key in algebra and helps solve equations more easily.
Remember: Understanding polynomial structure helps in performing further operations like addition, subtraction, multiplication, and even division.