Intermediate Algebra — 4.2: Factoring a² − b² скачать в хорошем качестве

Intermediate Algebra — 4.2: Factoring a² − b²

Learn to recognize and factor the difference of squares pattern, a² − b² = (a − b)(a + b). This lesson walks through the three-condition checklist for identifying difference of squares expressions, demonstrates why sums of squares don't factor over the integers, and extends the technique to expressions with coefficients and higher exponents. Key concepts covered: • The difference of squares formula: a² − b² = (a − b)(a + b) • Three-condition checklist: two terms, subtraction, and both terms must be perfect squares • FOIL verification showing why middle terms always cancel • Perfect squares reference: squares of 1 through 10 • Why sums of squares (like y² + 64) do not factor over the integers • Why non-perfect-square terms (like 15) break the pattern • Factoring with coefficients: treating 4y² as (2y)² and 25x² as (5x)² • Higher exponents using the power-of-a-power rule: rewriting x⁴ as (x²)² and y¹⁴ as (y⁷)² • Decision flowchart for difference of squares identification • Preview of sum and difference of cubes as the next factoring pattern ━━━━━━━━━━━━━━━━━━━━━━━━ SOURCE MATERIALS The source materials for this video are from    • Intermediate Algebra Lecture 6.5:  Factori...