Factoring

(𝑎+𝑏)² = 𝑎²+2𝑎𝑏+𝑏²
(𝑎-𝑏)² = 𝑎²-2𝑎𝑏+𝑏²
 𝑎²+𝑏² = (𝑎 - √2𝑎𝑏̚ + 𝑏)·(𝑎 + √2𝑎𝑏̚ + 𝑏)
 𝑎²-𝑏² = (𝑎 + 𝑏)·(𝑎 - 𝑏)
(𝑥-𝑎)(𝑥-𝑏) = 𝑥² - (𝑎+𝑏)𝑥 + 𝑎𝑏
(𝑎𝑥+𝑏)² = 𝑎²𝑥² + (2𝑎𝑏)𝑥 + 𝑏²
(𝑥+1)² = 𝑥² + 2𝑥 + 1
(𝑥-1)² = 𝑥² - 2𝑥 + 1

(𝑎+𝑏)³ = 𝑎³ + 3𝑎²𝑏 + 3𝑎𝑏² + 𝑏³
𝑎³+𝑏³ = (𝑎+𝑏)·0(𝑎²-𝑎𝑏+𝑏²)
(𝑥-𝑎)(𝑥-𝑏)(𝑥-𝑐) = 𝑥³-(𝑎+𝑏+𝑐)𝑥² + (𝑎𝑏+𝑏𝑐+𝑎𝑐)𝑥-𝑎𝑏𝑐



(𝑎+𝑏)ⁿ = Cⁿ₀ 𝑎ⁿ + Cⁿ₁ 𝑎ⁿ⁻¹𝑏 .+.  Cⁿₙ₋₁ 𝑎𝑏ⁿ⁻¹ +  Cⁿₙ 𝑏ⁿ

 Cⁿ₀ : n! /
         / (n-k)k!