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References: Foundations of Algebra

  1. Order of Operations - Wikipedia - Explains the standardized sequence (PEMDAS/BODMAS) for evaluating mathematical expressions with multiple operations, the core rule this chapter uses to evaluate and simplify expressions correctly.

  2. Algebraic Expression - Wikipedia - Defines how variables, constants, coefficients, and operations combine into algebraic expressions, directly supporting the chapter's coverage of terms, expressions, and expression structure.

  3. Distributive Property - Wikipedia - Describes the property \(a(b+c) = ab + ac\) that underlies expanding and factoring expressions, the technique used throughout the chapter's expanding-expressions section.

  4. Larson, Ron, and Laurie Boswell. Big Ideas Math: Algebra 1. Big Ideas Learning, 2019. Print. - Covers algebraic vocabulary, order of operations, evaluating expressions, and simplifying expressions with the guided-practice approach used in this chapter.

  5. Carter, John A., Gilbert J. Cuevas, et al. Glencoe Algebra 1: Common Core Edition. McGraw-Hill Education, 2012. Print. - A widely used Algebra 1 text with chapters on expressions, order of operations, properties of real numbers, and combining like terms that parallel this chapter's scope.

  6. Commutative, Associative and Distributive Laws - Math is Fun - Clear, example-driven explanation of the distributive law and related number properties, useful for understanding how to expand expressions like \(3(x+2)\) as covered in the chapter.

  7. Like Terms - Math is Fun - Defines like terms as terms sharing identical variable parts and shows worked examples of combining them, matching the chapter's like-terms and combining-like-terms sections.

  8. Order of Operations - Purplemath - Step-by-step lessons on applying PEMDAS to expressions with parentheses and exponents, reinforcing the chapter's order-of-operations rules and worked examples.

  9. Substitution - GeeksforGeeks - Explains substitution as replacing variables with known values to evaluate expressions and check equation solutions, directly supporting the chapter's substitution and evaluating-expressions sections.

  10. Prime Factorization - GeeksforGeeks - Describes methods for breaking numbers into prime factors using factor trees, supporting the chapter's prime factorization section and its connection to finding GCFs and factoring.