Basic Binomials

Expanding:

(a + b)² = (a + b)(a + b) = (a² + 2ab + b²)
(a - b)² = (a - b)(a - b) = (a² - 2ab + b²)
(a - b)² = (a - b)(a - b) = (a² + 2ab + b²)
(a² - b²) = (a + b)(a – b)
(a + b)³ = (a + b)(a + b)(a + b) = (a³ + 3a²b + 3ab² + b³)
a(a -1) = a² - a
3(b + 1) = 3b + 3

Factoring:

(a² + 2ab + b²) = (a + b)(a + b) = (a + b)²
(a² - 2ab + b²) = (a - b)(a - b) = (a - b)²
(a² + 2ab + b²) = (a - b)(a - b) = (a - b)²
(a + b)(a – b) = (a² - b²)
(a³ + 3a²b + 3ab² + b³) = (a + b)(a + b)(a + b) = (a + b)³
a² - a = a(a -1)
3b + 3 = 3(b + 1)

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