📚 Topic Summary
Multiplying monomials involves multiplying the coefficients and adding the exponents of like variables. For example, to multiply $3x^2$ by $4x^3$, you multiply the coefficients (3 and 4) to get 12, and add the exponents of $x$ (2 and 3) to get 5. The result is $12x^5$. Remember the rules of exponents: when multiplying powers with the same base, you add the exponents. This principle is fundamental to simplifying expressions involving monomials. Understanding and consistently applying this rule will greatly improve your proficiency in algebra.
When working with multiple variables, apply the same principle to each variable separately. For example, to multiply $2x^2y$ by $5xy^3$, multiply the coefficients (2 and 5) to get 10, add the exponents of $x$ (2 and 1) to get 3, and add the exponents of $y$ (1 and 3) to get 4. The result is $10x^3y^4$. Keep practicing, and you'll become a pro in no time!
🧮 Part A: Vocabulary
Match each term with its definition:
| Term |
Definition |
| 1. Coefficient |
a. A value that does not change |
| 2. Variable |
b. A term consisting of a number only |
| 3. Constant |
c. A symbol representing an unknown value |
| 4. Exponent |
d. A number placed above and to the right of a mathematical expression to denote the power to which the expression is to be raised |
| 5. Monomial |
e. A number multiplied by a variable in an algebraic expression |
Match the correct definition to the term. Example answer: 1-E.
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided below:
When multiplying monomials, you multiply the ________ and add the ________ of like variables. For example, in the expression $5x^3$, the 5 is the ________, and the 3 is the ________. A ________ is a single term expression.
Word Bank: coefficients, exponents, monomial, coefficient, exponent
🤔 Part C: Critical Thinking
Explain in your own words why you can add exponents when multiplying monomials with the same base. Use an example to illustrate your explanation.