Algebra 2: 4.4 Factoring - Difference of Two Squares & the Sum/Difference of Two Cubes

Difference of 2 squares

a² - b² —> (a + b)(a - b)

Zero-Product Property

If the product of two factors is zero, then at least one of the factors must be zero (if ab = 0, then a = 0, or b = 0, or both a = 0 and b = 0)

Sum of cubes

a³ + b³ = (a + b)(a² – ab + b²) (SIGNS: SAME, OPPOSITE, ALWAYS POSITIVE)

Difference of cubes

a³ - b³ = (a - b)(a² + ab + b²) (SIGNS: SAME, OPPOSITE, ALWAYS POSITIVE)