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Section 1.8

Section 1.8. Simplifying and Writing Algebraic Expressions. Page 71. Terms. A term is a number, a variable, or a product of numbers and variables raised to powers. Examples of terms include 4, z , 5 x , and −6 xy 2 .

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Section 1.8

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  1. Section 1.8 • Simplifying and Writing Algebraic Expressions

  2. Page 71 Terms • A term is a number, a variable, or a product of numbers and variables raised to powers. Examples of terms include • 4, z, 5x, and −6xy2. • The coefficient of a term is the number that appears in the term.

  3. Example Page 72 • Determine whether each expression is a term. If it is a term, identify its coefficient. • a. 97 b. 17x c. 4a – 6b d. 9y2 • Solution • a. A number is a term. The coefficient is 97. • b. The product of a number and a variable is a term. The coefficient is 17. • c. The difference of two terms in not a term. • d. The product of a number and a variable with an exponent is a term. Its coefficient is 9.

  4. Example Page 72 • Determine whether the terms are like or unlike. • a. 9x, −15xb. 16y2, 1 c. 5a3,5b3 d. 11, −8z • Solution • a. The variable in both terms is x, with the same power of 1, so they are like terms. • b. The term 1 has no variable and the 16 has a variable of y2. They are unlike terms. • c. The variables are different, so they are unlike terms. • d. The term 11 has no variable and the −8 has a variable of z. They are unlike terms.

  5. Example Page 73 • Combine terms in each expression, if possible. • a. −2y + 7y b. 4x2 – 6x • Solution • a. Combine terms by applying the distributive property. • −2y + 7y = (−2 + 7)y = 5y • b. They are unlike terms, so they can not be combined.

  6. Example Page 74 • Simplify each expression. • a. 13 + z – 9 + 7z b. 9x – 2(x – 5) • Solution • a. 13 + z – 9 + 7z b. 9x – 2(x – 5) = 13 +(– 9) + z + 7z = 9x + (– 2)x + (−2)(– 5) = 13 +(– 9) + (1+ 7)z = 9x – 2x + 10 = 7x+ 10 = 4 + 8z

  7. Example Page 74 • Simplify each expression. • a. 6x2 – y + 9x2 – 3y b. • Solution • a. 6x2 – y + 9x2 – 3y = 6x2 + 9x2 + (–1y) + (–3y) = (6 + 9)x2 + (–1+ (– 3))y Optional step = 15x2 –4y

  8. Example Page 74 • Simplify each expression. • a. 6x2 – y + 9x2 – 3y b. • Solution • b.

  9. 11 ft w 4 ft 18 ft Example Page 76 • A sidewalk has a constant width w and comprises several short sections with lengths 11, 4, and 18 feet. • a. Write and simplify an expression that gives the number of square feet of sidewalk. • b. Find the area of the sidewalk if its width is 3 feet. • Solution • a. 11w + 4w + 18w • = (11 + 4 + 18)w • = 33w • b. 33w = 33 ∙ 3 = 99 square feet

  10. End of chapter problems • do 56, 58, 72 on page 77 • do 74, 76, 78 on page 77-78 • do 80, 82 on page 78 • do 84, 86, 88 on page 78

  11. DONE

  12. Objectives • Terms • Combining Like Terms • Simplifying Expressions • Writing Expressions

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