# Algebraic Expressions

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### MATH 1 - Algebraic Expressions:

MATH 1 - Algebraic Expressions Arnie Dris

### Instructions for Preparation:

Instructions for Preparation Write your name and course section in a ¼ sheet of yellow pad paper. You will be writing answers to questions in this presentation as we go along.

### Definition – Algebraic Expression:

Definition – Algebraic Expression AN ALGEBRAIC EXPRESSION is a combination of ordinary numbers and letters which represent numbers (called variables ). Thus 3 x 2 – 5 xy + 2 y 4 and 2 a 3 b 5 are algebraic expressions.

### Definition - Term:

Definition - Term A TERM consists of products and quotients of ordinary numbers and letters which represent numbers (i.e. variables). Thus, 6 x 2 y 3 , 5 x /3 y 4 and –3 x 7 are terms. However, 6 x 2 + 7 xy is an algebraic expression consisting of two terms.

### Definition - Monomial:

Definition - Monomial A MONOMIAL is an algebraic expression consisting of only one term. Thus 7 x 3 y 4 , 3 xyz 2 and 4 x 2 / y are monomials. Because of this definition, monomials are sometimes simply called terms.

### Seatwork Item #1:

Seatwork Item #1 Which of the following is a monomial? 2 x + 4 y 3 x 2 – 5 x + 2 4 x 2 / y 3 x 3 + 6 x 2 y – 7 xy + 6 None of the above

### Definition - Binomial:

Definition - Binomial A BINOMIAL is an algebraic expression consisting of two terms. Thus, 2 x + 4 y and 3 x 4 – 4 xyz 3 are binomials.

### Seatwork Item #2:

Seatwork Item #2 Which of the following is a binomial? 3 x 2 – 5 x + 2 2 x + 4 y 3 x 3 + 6 x 2 y – 7 xy + 6 4 x 2 / y None of the above

### Definition - Trinomial:

Definition - Trinomial A TRINOMIAL is an algebraic expression consisting of three terms. Thus 3 x 2 – 5 x + 2, 2 x + 6 y – 3 z and x 3 – 3 xy / z – 2 x 3 z 7 are trinomials.

### Seatwork Item #3:

Seatwork Item #3 Which of the following is a trinomial? 3 x 2 – 5 x + 2 2 x + 4 y 3 x 3 + 6 x 2 y – 7 xy + 6 4 x 2 / y None of the above

### Definition - Multinomial:

Definition - Multinomial A MULTINOMIAL is an algebraic expression consisting of more than one term. Thus 7 x + 6 y , 3 x 3 + 6 x 2 y – 7 xy + 6 and 7 x + 5 x 2 / y – 3 x 3 /16 are multinomials.

### Seatwork Item #4:

Seatwork Item #4 Which of the following is a multinomial? 3 x 2 – 5 x + 2 2 x + 4 y 3 x 3 + 6 x 2 y – 7 xy + 6 x 3 – 3 xy / z – 2 x 3 z 7 All of the above

### Definition - Coefficient:

Definition - Coefficient COEFFICIENT. One factor of a term is said to be the coefficient of the rest of the term. Thus in the term 5 x 3 y 2 , 5 x 3 is the coefficient of y 2 , 5 y 2 is the coefficient of x 3 , and 5 is the coefficient of x 3 y 2 .

### Seatwork Item #5:

Seatwork Item #5 In the term 13 WXYZ , what is the coefficient of 13 W ? In the term AB 2 C 3 D 4 E 5 , what is the coefficient of ABCDE ? In the term AB 2 C 3 D 4 E 5 , what is the coefficient of BC 2 D 3 E 4 ? 