Operations with Monomials Operations with Polynomials

Monomial A number, a variable or a product of a number and variable(s) Examples: ½ x A y 3 2x 5xyz -3x 2 4xy 3 ¼ x 3 Not Monomials 2x + 4 4x – 5 Isn’t this the same as

Quick Review base Exponent or power Coefficient

The Laws of Exponents: Multiplicative Law of Exponents: When multiplying monomials and the bases are the same: multiply the coefficients and add the exponents. Here is why this works…lets break the example down

Example #1 (3x 2 )(-6x 3 ) -18 Example #2 (4y 2 z 2 )(y 3 ) 1. Multiply the coefficients 2. Write down the bases in alphabetical order 3. Add the exponents of the like bases 1. Multiply the coefficients 2. Write down the bases in alphabetical order 3. Add the exponents of the like bases 4. Bring down any other exponents

Practice

The Laws of Exponents: Exponential Law of Exponents: to raise a monomial to a power - raise the coefficient to the power - Multiply the exponents

The Laws of Exponents: Exponential Law of Exponents: to raise a monomial to a power - raise the coefficient to the power - Multiply the exponents 1. 2 to the 4 th power = Write the variables down 3. Multiply each variables exponent time the exponent on the outside of the parentheses

Practice

The Laws of Exponents: Division Law of Exponents: When dividing monomials: - simplify the coefficients - subtract the exponents with same bases - Simpify any Negative or Zero exponents

The Laws of Exponents: Division Law of Exponents: When dividing monomials: - simplify the coefficients - subtract the exponents with same bases - Simpify any Negative or Zero exponents

Practice

Binomial – 2 monomials connected by addition or subtraction Trinomial – 3 monomials connected by addition or subtraction Polynomial – 1 or more monomials connected by addition or subtraction Like Terms – have the same variable and the same exponent

Add Polynomials – ignore the parentheses and combine like terms 1. Combine the term with the biggest exponent 2. Then combine the terms with next biggest exponent 3. Continue combing terms in descending order

Subtract Polynomials – distribute the negative 1 and combine like terms 1. Distribute the negative 1 (turn everything to its opposite) 2. Cross out the 2 nd parentheses of original problem 3. Combine like terms, going in descending order

Add Polynomials – ignore the parentheses and combine like terms 1. Combine the term with the biggest exponent 2. Then combine the terms with next biggest exponent 3. Continue combining terms in descending order Subtract Polynomials – distribute the negative 1 and combine like terms 1. Distribute the negative 1 (turn everything to its opposite) 2. Cross out the 2 nd parentheses of original problem 3. Combine like terms, going in descending order