Understanding the Expression 3x³ + 2x² + 48x²: Factoring and Simplifying Algebraic Terms
Algebraic expressions often combine coefficients, variables, and exponents in ways that require careful analysis. Which means the expression 3x³ + 2x² + 48x² serves as an excellent example to explore factoring techniques and combining like terms. This article will guide you through simplifying the expression step by step, explain the underlying mathematical principles, and address common questions related to algebraic manipulation.
Introduction to the Expression
The given expression, 3x³ + 2x² + 48x², includes three terms with varying degrees of the variable x. But the first term, 3x³, has an exponent of 3, while the second and third terms, 2x² and 48x², both have an exponent of 2. The goal is to simplify this expression by combining like terms and factoring where possible.
Key Concepts Involved:
- Like Terms: Terms with the same variable raised to the same exponent.
- Combining Like Terms: Adding or subtracting coefficients of like terms.
- Factoring: Expressing an algebraic expression as a product of simpler terms.
Step-by-Step Simplification
Step 1: Identify Like Terms
In the expression **3x
