(3a – 5b)2 = (3a)2-2·3a·5b + (5b)2 = 9a2 – 30ab + 25b2
(x + 2y)2 = x2 + 2 ·x·2y + (2y)2 = x2 + 4xy + 4y2
9x2 – 16y2 = (3x)2 – (4y)2 = (3x – 4y)(3x + 4y)
(3x + 2y)3 = (3x)3 + 3·(3x)2·2y + 3·3x·(2y)2 + (2y)3 = 27x3 + 54x2y + 36xy2 + 8y3
(2x – y)3 = (2x)3-3·(2x)2·y + 3·2x·y2 – y3 = 8x3 – 12x2y + 6xy2 – y3
125 + 8x3 = 53 + (2x)3 = (5 + 2x)(52 — 5·2x + (2x)2) = (5 + 2x)(25 – 10x + 4x2)
64с3 – 8 = (4с)3 – 23 = (4с – 2)((4с)2 + 4с·2 + 22) = (4с – 2)(16с2 + 8с + 4)
(3a – 5b)(9a2 + 15ab + 25b2) = (3a)3 – (5b)3 = 27a3 – 125b3
(1 + 3m)(1 – 3m + 9m2) = 13 + (3m)3 = 1 + 27m3
(x – 3n)3 = x3-3·x2·3n + 3·x·(3n)2 – (3n)3 = x3 – 9x2n + 27xn2 – 27n3