Скачать или смотреть Intermediate Algebra — 4.4: Sum and Difference of Cubes

Learn to factor expressions like x³ − 64 and x³ + 27 using the cube factoring formulas and the SOAP mnemonic (Same, Opposite, Always Positive). This lesson walks through five progressively challenging examples—from simple single-variable cubes to expressions with coefficients and two variables—building fluency with a pattern that works every time.

Key concepts covered:
• Perfect cubes to memorize: 1, 8, 27, 64, 125 and their cube roots
• The two cube factoring formulas: a³ − b³ = (a − b)(a² + ab + b²) and a³ + b³ = (a + b)(a² − ab + b²)
• The SOAP mnemonic: Same sign, Opposite sign, Always Positive
• Identifying the binomial (small factor) and trinomial (big factor)
• The most common error: forgetting to square the entire coefficient, e.g., (4y)² = 16y², not 4y²
• Factoring with coefficients on both terms, such as 64y³ − 1 and 27x³ + 8
• Two-variable cube factoring: 125x³ − 64y³
• Verification by expanding the factored form back to the original
• The complete two-term factoring toolkit: difference of squares, difference of cubes, sum of cubes, and why sum of squares is not factorable over the reals
• A decision flowchart: extract the GCF first, then determine squares vs. cubes and addition vs. subtraction

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SOURCE MATERIALS
The source materials for this video are from    • Intermediate Algebra Lecture 6.5:  Factori...