Verified answer

1a) ay - 12bx + 3ax - 4by = (ay - 4by) + (3ax - 12bx) = y(a - 4b) + 3x(a - 4b) = (a - 4b)(y + 3x)

1б) x² - 8x + 15 = (x - 5)(x - 3)

2a) (y - 5)² - ( y - 2)5y = y² - 10y + 25 - 5y² + 10y = - 6y² + 25

2б) - 4(p - 2a)² = -4(p² - 4ap + 4a²) = - 4p² + 16ap - 16a²

3a) 16x² + 8xy + y² = (4x + y)²

3б) 49p² - 14p + 1  = (7p - 1)²

4a) (3 - 1/5a)(3 + 1/5a) = 3² - (1/5a)² = 9 - 1/25a² = 9 - 0,04a²

4б) (5b² + 1)(1 - 5b²) = 1² - (5b²)² = 1 - 5b⁴

5a) x²y⁴ - 1 = (xy²)² - 1² = (xy² - 1)(xy² + 1)

5б) 81 - 64x²y² = 9² - (8xy)² = (9 - 8xy)(9 + 8xy)