1a) (m + 7)² - (m - 7)² = m² + 14m + 49 - (m² - 14m + 49) =
= m² + 14m + 49 - m² + 14m - 49 = 28m
1б) 8a² - (a +5)² = 8a² - (a² + 10a + 25) = 8a² - a² - 10a - 25 = 7a² - 10a - 25
1в) (c + 3)² - (c - 4)(c + 4) = c² + 6c + 9 - c² + 16 = 22c + 9
1г) (x + 6)² - x(x - 12) = x² + 12x + 36 - x² + 12x = 24x + 36
2a) (2x - 5)² - (2x - 3)(2x + 3) = 0
4x² - 20x + 25 - 4x² + 9 = 0
- 20x + 34 = 0
- 20x = - 34
x = 1,7
2б) (x + 1)² - (2x - 1)² = 0
x² + 2x + 1 - 4x² + 4x - 1 = 0
- 3x² + 6x = 0
x² - 2x = 0
x(x - 2) = 0
x₁ = 0 x - 2 = 0
x₂ = 2
2в) (x - 6)² -x(x + 8) = 2
x² - 12x + 36 - x² - 8x = 2
- 20x = 2 - 36
- 20x = - 34
x = 1,7
2г) (y - 2)² = y(y + 2)
y² - 4y + 4 - y² - 2y = 0
- 6y + 4 = 0
- 6y = - 4
y = 2/3
3a) 49a² - 25b² = (7a)² - (5b)² = (7a - 5b)(7a + 5b)
3б) 27x³ - 8 = (3x)³ - 2³ = (3x - 2)(9x² + 6x + 4)
3в) 125x³ + 64y³ = (5x)³ + (4y)³ = (5x + 4y)(25x² - 20xy + 16y²)
3г) (3x - 7)² = (3x - 7)(3x - 7)