Intermediate Algebra — 7.4: Sum and Difference of Cubes

Описание: Learn how to factor cubic expressions using the "Same, Different, Plus" mnemonic — a three-word pattern that makes both sum and difference of cubes as automatic as difference of squares. The video also covers factoring by grouping for four-term polynomials and builds a complete decision flowchart for simplifying rational expressions.

Key concepts covered:
• Perfect cubes and recognizing cubic patterns (1, 8, 27, 64, 125)
• Sum of cubes formula: a³ + b³ = (a + b)(a² − ab + b²)
• Difference of cubes formula: a³ − b³ = (a − b)(a² + ab + b²)
• The "Same, Different, Plus" sign pattern for both formulas
• Why sum of squares (a² + b²) does not factor over the real numbers
• Factoring by grouping: splitting four-term polynomials into pairs and extracting the GCF
• The critical distinction between cancelling multiplicative factors vs. additive terms
• A decision flowchart: 2 terms → squares or cubes, 3 terms → diamond method, 4 terms → grouping
• Worked example: simplifying (x³ + 27)/(x + 3) step by step

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SOURCE MATERIALS
The source materials for this video are from    • Intermediate Algebra Lecture 7.1:  Definin...