Worksheet -: Algebraic Expressions What is a constant? A Constant is a number representing a quantity or value that does not change. What is a variable? A variable is a letter or symbol representing a quantity or value that can vary or change. What is an algebraic expression? Algebraic expression is a mathematical expression containing a variable. Forms of Algebraic Expressions:. One Variable Term : x, y. Variable Term + Constant Term: x +, 5 + y. Variable Term Constant Term: x, 5 y. Variable Term + Variable Term: x + y, 5 a + b 5. Variable Term Variable Term: x y, 5a b Constant Term = A Number (A whole number, a decimal number or a fraction) Forms of Constant Terms: (Can be Positive or Negative). Whole Number Form: x +. Decimal Form: x 0.. Fraction Form: y + 7
Variable Term = Coefficient x Variable WS - The variable term has two parts: Numerical part (Coefficient) and Letter part (Variable) Coefficient is the numerical part of the variable term. x² x² Variable is the alphabetical letter part of the variable term, including any exponent. ** When the coefficient is, we do not write before the variable. Forms of Variable Terms:. Product Form: y, x, 7a. Quotient Form: x, 0.79y, a. Exponent Form: x, y, x y. For the following algebraic expressions, name the constant term, the variable term and the coefficient of the variable term. (a) x + Constant term = Variable term = x Coefficient = (b) y (c) 7 a +. 5 (d) 7.5b 7 7 (e) + a 5 5 (f) h (g) a + (h) x
Worksheet -: Polynomials Monomials The basic building blocks for algebraic expressions are called the monomials. Each term in an algebraic expression is a monomial. A monomial is a number or a variable or the product of numbers and variables. e.g., 5,, 800 are monomials that are numbers. e.g., t, a, x are monomials that are variables. e.g., r, 7a, xy, t², 8st are monomials that are products of numbers and variables. Polynomials A polynomial is a monomial or a sum of monomials. A polynomial is formed by adding or subtracting monomials. e.g., 9, y, a + 8, s t, x x + 9, a + b + c d Classifying Polynomials by Number of Terms Polynomials are classified by the number of terms. Monomials are polynomials that have only one term such as x y, 8, 0m,, Binomials are polynomials that have two terms such as x +, a b, s + st. Trinomials are polynomials that have three terms such as a + a + a, x + x, x + y. Polynomials that have four or more terms are just called polynomials such as x + 6x x +. a Name of Algebraic Expression Number of Terms -Term Polynomial 5 6 00
Classifying Polynomials by Number of Terms Recall: Monomials have ONE term. Binomials have TWO terms. Trinomials have THREE terms. Polynomials have FOUR or MORE terms. (Hint: Monopoly one owner) (Hint: Bicycles two wheels) (Hint: Triangles three angles) (Hint: Poly means many) WS - Note: Monomials, binomials and trinomials are all polynomials. They are special names for polynomials with one to three terms. For polynomials with more than three terms (i.e. four or more), we don t have special names for them. They are just all called polynomials. Classify each algebraic expression as monomial, binomial, trinomial or polynomial.. x + 5. 8 y. 5a + 6a. z + 0z 5. 00 6. x 9x + 5x 7 7. x 8. s + s + 8 9. 6 e 0. y + y + y y +. p q. 9 b. x + 6x. ab 8 5. m 9 Answers:. binomial;. monomial;. trinomial;. binomial; 5. monomial; 6. polynomial; 7. binomial; 8. trinomial; 9. monomial; 0. polynomial;. binomial;. monomial;. trinomial;. binomial; 5. binomial.
Worksheet -: Like Terms vs. Unlike Terms Like terms have the same variables and exponents. e.g., y and 8 y are like terms. 5x and x are like terms. Why? Unlike terms have different variables or different exponents. e.g., x and 8 y are unlike terms. y and y are unlike terms. Why?. Connect the like terms with a straight line using a ruler. x 8 xyz z yz xyz y y z 8 x yz. Circle terms that are like x : 5x x x x y x 7 x x. Circle terms that are like x : 5x x x 9x x y x 7 x x. Provide each monomial with a like term and an unlike term. (a) 9 a (b) b (c) c