Розділ 3. Одночлени і многочлени » 38

Спростіть вираз двома способами: 1) (x + 3)2 – (x – 3)2; I (x + 3)2 – (x – 3)2 = (x + 3 – x + 3)(x + 3 + x – 3) = 6 • 2x = 12x; II (x + 3)2 – (x – 3)2 = x2 + 6x + 9 – x2 + 6x – 9 = 12x. 2) (x + 2)3 – (x – 2)3; I (x + 2)3 – (x – 2)3 = x3 + 3x2 • 2 + 3x • 23 + 23 – (x3 – 3x2 • 2 + 3x • 23 – 23) = x3 + 6x2 + 24x + 8 – x3 + 6x2 – 24x + 8 = 12x2 + 16 = 4(3x2 + 4); II (x + 2)3 – (x – 2)3 = (x + 2 – x + 2) • ((x + 2)2 + (x + 2)(x – 2) + (x – 2)2) = 4 • (x2 + 4x + 4 + x2 – 4 + x2 – 4x + 4) 4 • (3x2 + 4).