1.
1) (с - 6)² = с² - 12с + 36
2) (2a - 3b)² = 4a² - 12ab + 9b²
3) (5 - a)(5 + a) = 25 - a²
4) (5a + 8b)(8b - 5a) = 64b² - 25a²
2.
1) b² - 49 = (b - 7)(b + 7)
2) c² - 8c + 16 = (c - 4)²
3) 100 - 9x² = (10 - 3x)(10 + 3x)
4) 4a² + 20ab + 25b² = (2a + 5b)²
3. (x - 2)(x + 2) - (x - 5)² = x² - 4 - x² + 10x - 25 = 10x - 29
4.
4(3y + 1)² - 27 = (4y +9)(4y - 9) + 2(5y + 2)(2y - 7)
4 (9y² + 6y + 1) - 27 = 16y² - 81 + 2(10y² - 35y + 4y - 14)
36y² + 24y + 4 - 27 = 16y² - 81 + 2(10y² - 31y - 14)
36y² + 24y - 23 = 16y² - 81 + 20y² - 62y - 28
36y² + 24y - 23 = 36y² - 62y - 109
86y = -86
y = -1
5. (4b - 9)² - (3b + 8)² = (4b - 9 - 3b - 8)(4b - 9 + 3b + 8) = (b - 17)(7b - 1)
6. (3 - b)(3 + b)(9 + b²) + (4 + b²)², b = 1/2
(3 - b)(3 + b)(9 + b²) + (4 + b²)² = (9 - b²)(9 + b²) + 16 + 8b² + b⁴ = 81 - b⁴ + 16 + 8b² + b⁴ = 97 + 8b² = 97 + 8·(1/2)² = 97 + 2 = 99
7. x² - 14x + 51 = (x² - 14x + 49) + 2 = (x - 7)² + 2
(x - 7)² ≥ 0 ⇒ (x - 7)² + 2 > 0