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Algebra I – Monomials Polynomials and Factoring

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    Study Guide Algebra – Monomials Polynomials and Factoring 1. Monomials What is a Monomial? A monomial is an algebraic expression that has only one term . A term is a number, a variable, or a combination of numbers and variables that are multiplied together. Examples of Monomials • (9x) • (4a 2 ) • (3mpx 2 ) Each of these has only one term , so they are monomials. The number in front of the variable is called the numerical coefficient . Example: • In 9x , the coefficient is 9 . Adding and Subtracting Monomials When adding or subtracting monomials, you must follow one important rule: You can only combine like terms . What are Like Terms?

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    Study Guide Like terms have: • The same variables • The same exponents When terms are alike: • Add or subtract the coefficients • Keep the variables the same Example 1 Perform the operation: Step - by - step: 1. Divide the coefficients (15 ÷ - 3 = - 5) 2. The variables cancel because they are the same. Final Answer: Example 2 Both terms contain x , so they are like terms. Add the coefficients:

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    Study Guide Final Answer: Example 3 Step - by - step: 1. Divide the coefficients (9 ÷ - 3 = - 3) 2. (y) cancels out. Final Answer: Example 4 Step - by - step: 1. Combine like terms:

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    Study Guide 2. Subtract (3q): 3. Subtracting a negative becomes addition: Final Answer: Multiplying Monomials When multiplying monomials, remember this rule: Add the exponents when the base is the same. This rule comes from the laws of exponents. Examples Another example: Important Rule To multiply monomials:

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    Study Guide 1. Multiply the numbers (coefficients) 2. Add the exponents of variables with the same base. Example 2: Multiplying Monomials Multiply the following expressions. Problem 1 Add the exponents: Final Answer: Problem 2

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    Study Guide Add exponents of the same variables: Final Answer: Problem 3 Step 1: Multiply coefficients Step 2: Add exponents Final Answer: Problem 4

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    Study Guide Step 1: Multiply coefficients Step 2: Add exponents Final Answer: Problem 5 Add exponents: Final Answer: Problem 6

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    Study Guide Add exponents: Final Answer: Raising Monomials to a Power Sometimes a monomial is raised to a power. In this case: Multiply the exponents by the power. Example rule: This means every exponent inside the monomial gets multiplied by the power outside. Powers and Division of Monomials Example 3: Simplifying Powers Sometimes a monomial is raised to a power. To simplify expressions like this, we apply the rules of exponents . Rule

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    Study Guide When a power is raised to another power, multiply the exponents . Example 3 Simplify the following expressions. 1. Multiply the exponents: 2. Multiply each exponent by 4 : Final answer: 3.

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    Study Guide Apply the power to each part of the monomial: Final answer: Dividing Monomials When dividing monomials that have the same base , we use a simple rule. Rule Subtract the exponent of the divisor from the exponent of the dividend. Example 4: Dividing Monomials Divide the following expressions. Problem 1 Subtract the exponents:

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