1. а) (x² + 1)² = x⁴ + 2x² + 1² = x⁴ + 2x² + 1

б) (y² - 6)² = y⁴ - 24y² + 36

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а) (a³ + 3b)² = a⁹ + 6a³b + 9b²

б) (4x² - 3c)² = 16x⁴ - 48x²c + 9c²

2. а) (a - 4)² + а(а + 8) = а² - 8а + 16 + а² + 8а = 2а² + 16

в) (y - 5)² - (y - 2) = y² - 10y + 25 - y + 2 = y² - 11y + 27

3. а) (5а - 10)² - (3а - 8)² + 132a = 132

3.1 (5a - 10)² = (-30 - 10)² = (-40)² = 1600

3.2 (3a - 8)² = (-18 - 8)² = (-26)² = 676

3.3 132 * (-6) = -792

3.4 1600 - 676 - 792 = 132

4. б) x² + 4x + 5 = x² + 2 * 2x + 2² - 2² + 5 = (x + 2)² - 4 + 5 = (x + 2)² + 1

г) x² - 8x + 17 = x² - 2 * 4x + 4² - 4² + 17 = (x - 4)² - 16 + 17 = (x - 4)² + 1