(a+b)2 = a2+2ab+b2 пример (x + 2y)2 = x2 + 2 ·x·2y + (2y)2 = x2 + 4xy + 4y2
(a-b)2 = a2-2ab+b2 пример (3a – 5b)2 = (3a)2-2·3a·5b + (5b)2 = 9a2 – 30ab + 25b2
a2–b2 = (a–b)(a+b) пример 9x2 – 16y2 = (3x)2 – (4y)2 = (3x – 4y)(3x + 4y)
(a+b)3 = a3+3a2b+3ab2+b3 пример (m + 2n)3 = m3 + 3·m2·2n + 3·m·(2n)2 + (2n)3 = m3 + 6m2n + 12mn2 + 8n3
(a-b)3 = a3-3a2b+3ab2-b3 пример 125 + 8x3 = 53 + (2x)3 = (5 + 2x)(52 — 5·2x + (2x)2) = (5 + 2x)(25 – 10x + 4x2)