what is 5x times 3x 2 5

less than a minute read 26-12-2024

Decoding "5x times 3x + 2 + 5"

This article explains how to solve algebraic expressions like "5x times 3x + 2 + 5." We'll break down the process step-by-step, clarifying the order of operations and the rules of algebra involved. Understanding this type of problem is fundamental to mastering algebra.

Understanding the Expression

The expression "5x times 3x + 2 + 5" can be rewritten more clearly as: 5x * (3x + 2) + 5. The parentheses are crucial; they indicate that the 5x is multiplied by the entire expression (3x + 2), not just the 3x.

Order of Operations (PEMDAS/BODMAS)

Before we begin, remember the order of operations:

Parentheses/Brackets
Exponents/Orders
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

Step-by-Step Solution

Parentheses/Brackets: We address the expression within the parentheses first: There's nothing to simplify within (3x + 2), so we move to the next step.
Multiplication: Now, we multiply 5x by each term inside the parentheses:

5x * (3x + 2) = (5x * 3x) + (5x * 2) = 15x² + 10x
Addition: Finally, we add the remaining term:

15x² + 10x + 5

The Final Answer

Therefore, the simplified form of "5x times 3x + 2 + 5" is 15x² + 10x + 5. This is a quadratic expression, meaning it contains a variable raised to the power of 2 (x²).

Important Considerations

Variables: The 'x' represents an unknown value. We can't find a numerical answer unless we are given a specific value for 'x'.
Coefficients: The numbers in front of the variables (5, 3, 10, 15) are called coefficients. They represent the numerical factor of the term.
Terms: The parts of an expression separated by plus or minus signs are called terms (e.g., 15x², 10x, 5).
Like Terms: Like terms have the same variable raised to the same power (e.g., 5x and 10x). We can only combine like terms through addition or subtraction.

This example highlights the importance of understanding the order of operations and how to manipulate algebraic expressions. Mastering these fundamentals lays the groundwork for more advanced algebraic concepts.