Multiplying Monomials vs. Adding Monomials: What's the Difference?

📚 Multiplying Monomials vs. Adding Monomials: What's the Difference?

Monomials are algebraic expressions consisting of one term. These terms can include numbers, variables, and exponents. The key difference between multiplying and adding monomials lies in how you handle the coefficients and exponents.

➕ Definition of Adding Monomials

Adding monomials involves combining like terms. Like terms have the same variables raised to the same powers. When adding, you only add the coefficients; the variables and their exponents remain unchanged.

• 🔍 Like Terms: Terms that have the same variable(s) raised to the same power. For example, $3x^2$ and $5x^2$ are like terms.
• 💡 Adding Coefficients: When adding like terms, add their coefficients. For example, $3x^2 + 5x^2 = (3+5)x^2 = 8x^2$.
• 📝 Unlike Terms: Unlike terms cannot be combined directly. For example, $3x^2$ and $5x$ are unlike terms. The expression $3x^2 + 5x$ remains as is.

✖️ Definition of Multiplying Monomials

Multiplying monomials involves multiplying the coefficients and adding the exponents of like variables. Unlike adding, you can multiply terms even if they are not 'like' terms.

• 🧮 Multiplying Coefficients: Multiply the numerical coefficients. For example, in $(3x^2)(5x)$, multiply 3 and 5 to get 15.
• 🧪 Adding Exponents: Add the exponents of the same variables. For example, in $(3x^2)(5x)$, add the exponents of $x$: $2+1 = 3$.
• 🧬 Result: Combining these steps, $(3x^2)(5x) = 15x^3$.

📊 Comparison Table

💡 Key Takeaways

• 🔑 Adding: Only add coefficients of like terms; exponents stay the same. Example: $7y^3 + 2y^3 = 9y^3$.
• ✍️ Multiplying: Multiply coefficients and add exponents of like variables. Example: $(4a^2)(6a^4) = 24a^6$.
• 🌍 Remember: Adding requires like terms, while multiplying does not.
• 🔢 Practice: Consistent practice will solidify your understanding!