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Understanding Expressions: Terms and Coefficients

Learn to differentiate terms and coefficients in algebraic expressions, and evaluate expressions by substituting values and following order of operations. Explore factors vs. terms and practice simplifying expressions. Understand the significance of maintaining a consistent order of operations.

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Understanding Expressions: Terms and Coefficients

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  1. REFLECT

  2. 1a. Write the expression 3n – 4n – 8 as a sum. How does this help you identify the terms of the expression? Identify the terms. 3m + (-4n) + (-8) Writing an expression as a sum clarifies the parts being added and their signs. 3m, -4n, -8

  3. 1b. Explain and illustrate the difference between a term and a coefficient. A term is a part of an expression being added. A coefficient is a numerical factor of a term. Ex. 4x is a term of 4x + 1. Its coefficient is 4.

  4. 1c. What is the coefficient of x in the expression x - 2? Explain your reasoning. 1 x = 1∙x  so the numerical factor of the term is 1.

  5. 1d. What is the value of 1-18+25 if you subtract then add? If you add then subtract? Why is the order of operations necessary? Subtract and then add  8 Add then subtract  -42 Results will vary if a consistent order is NOT followed.

  6. VOCABULARY evaluate An algebraic expression – substitute the value(s) of the variable(s) into the expression and simplify using the order of operations

  7. REFLECT - Part 2 2a. Explain why x and 4x - 10 are factors of the expression x(4x - 10)3 rather than terms of the expressions. What are the terms of the factors 4x – 10. The expressions x and 4x – 10 are multiplied, not added, to form x(4x-10)3, which makes them factors, not terms 4x, -10

  8. 2b. Evaluate 5a + 3b and (5 + a)(3 + b) for a = 2 and b = 4. How is the order of the steps different for the two expressions? 5a + 3b 22  Multiply first then add (5 + a)(3 + b) 49  Add first then multiply

  9. 2c. In what order would you perform the operations to correctly evaluate the expression 2 + (3 – 4)∙9? What is the result. Subtract, then multiply, then add  -7

  10. 2d. Show how to move the parentheses in the expression 2 + (3 – 4)∙9 so that the value of the expression is 9. ( 2 + 3 – 4) ∙ 9

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