Chapter 2 Equations, Inequalities and Problem Solving

§ 2.1 Simplifying Algebraic Expressions

Martin-Gay, Beginning Algebra, 5ed 33 Terms A term is a number, or the product of a number and variables raised to powers – (the number is called a coefficient). Examples of Terms 7 (coefficient is 7) 5x 3 (coefficient is 5) 4xy 2 (coefficient is 4) z 2 (coefficient is 1)

Martin-Gay, Beginning Algebra, 5ed 44 Like terms contain the same variables raised to the same powers. To combine like terms, add or subtract the numerical coefficients (as appropriate), then multiply the result by the common variable factors. You can combine like terms by adding or subtracting them (this is not true for unlike terms). Like Terms

Martin-Gay, Beginning Algebra, 5ed 55 6x 2 + 7x 2 19xy – 30xy 13xy 2 – 7x 2 y 13x 2 – 11xy Can’t be combined (since the terms are not like terms) Examples of Combining Terms Terms Before CombiningAfter Combining Terms Combining Like Terms

Martin-Gay, Beginning Algebra, 5ed 66 a.) 2(x + y) = 2x + 2y Example: Find each product by using the distributive property to remove the parentheses. Using the Distributive Property b.) 7(x + 2y – 5z) = 7x + 14y – 35z c.) – 4(3a – 3b – 10c) = – 12a + 12b + 40c a.) 2(x + y) b.) 7(x + 2y – 5z)c.) – 4(3a – 3b – 10c)

Martin-Gay, Beginning Algebra, 5ed 77 Word Phrases as Algebraic Expressions Addition (+) Subtraction (–) Multiplication (·) Division (  ) sum plus added to more than increased by total difference minus subtract less than decreased by less product times multiply multiplied by of double/triple quotient divide shared equally among divided by divided into

Martin-Gay, Beginning Algebra, 5ed 88 Word Phrases as Algebraic Expressions Example: Write as an algebraic expression. Use x to represent “a number.” In words: a.) 5 decreased by a number b.) The quotient of a number and 12 5 Translate: 5 decreased bya number –x a.) In words: a number Translate: x and12  b.) The quotient of