10 примеров формулы сокращенного умножения

(3a - 5b) 2 = (3a) 2-2·3a·5b + (5b) 2 = 9a 2 - 30ab + 25b 2

(x + 2y) 2 = x 2 + 2 ·x·2y + (2y) 2 = x2 + 4xy + 4y 2

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 = 27x 3 + 54x 2y + 36xy2 + 8y 3

(2x - y) 3 = (2x) 3-3· (2x) 2·y + 3· 2x·y2 - y3 = 8x 3 - 12x 2y + 6xy2 - y 3

125 + 8x3 = 53 + (2x) 3 = (5 + 2x) (52 - 5·2x + (2x) 2) = (5 + 2x) (25 - 10x + 4x2)

64 с3 - 8 = (4 с) 3 - 23 = (4 с - 2) ((4 с) 2 + 4 с·2 + 22) = (4 с - 2) (16 с2 + 8 с + 4)

(3a - 5b) (9a2 + 15ab + 25b 2) = (3a) 3 - (5b) 3 = 27a 3 - 125b 3

(1 + 3m) (1 - 3m + 9m2) = 13 + (3m) 3 = 1 + 27m 3

(x - 3n) 3 = x3-3·x2·3n + 3· x· (3n) 2 - (3n) 3 = x 3 - 9x 2n + 27xn2 - 27n 3