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Answer:
1. ax + bx - ay - by
x × (a + b) - y × (a + b)
= (a + b) × (x - y)
2. 3b² - ab² - 3c² + ac²
b² × (3 - a) - c² × (3 - a)
(3 - a) × (b² - c²)
= (3 - a) × (b - c) × (b + c)
3. 12x² + x - 4x³ - 3
4x² × (3 - x) - (3 - x)
(3 - x) × (4x² - 1)
= (3 - x) × (2x - 1) × (2x + 1)
4. 2a + 15ab - 20a - 21b
-18a + 15ab - 21b
= -3(6a - 5ab + 7b)
5. 3pq + 4 - 2q - 6p
q × (3p - 2) - 2(-2 + 3p)
= (3p - 2) × (q - 2)
6. 4x² - y² + 2x + y
(2x - y) × (2x + y) + 2x + y
= (2x + y) × (2x - y + 1)
7. a³ - a²b + a²c - a + b - c
a² × (a - b + c) - (a - b + c)
(a - b + c) × (a² - 1)
= (a - b + c) × (a - 1) × (a + 1)
8. x⁴ - x³y - x + y
x³ × (x - y) - (x - y)
(x - y) × (x³ - 1)
= (x - y) × (x - 1) × (x² + x + 1)
9. (1 + xy)² - (x + y)²
(1 + xy - (x + y)) × (1 + xy + (x + y))
(1 + xy - x - y) × (1 + xy + x + y)
(- (x - 1) + y × (x - 1)) × (1 + y × (x + 1) + x)
(- (x - 1) × (1 - y)) × (x + 1) × (1 + y)
= - (x - 1) × (1 - y) × (x + 1) × (1 + y)
10. 36x² - y² + 6yz - 9z²
36x² - (y² - 6yz + 9z²)
36x² - (y - 3z)²
(6x - (y - 3z)) × (6x + (y - 3z))
= (6x - y + 3z) × (6x + y - 3z)
11. 4d(a - 8) + y(a - 8)
= (a - 8) × (4d + y)
12. xy - 5x + 2y - 10
x × (y - 5) + 2(y - 5)
= (y - 5) × (x + 2)
13. 4ax + 14bx - 6ay - 21by
2x × (2a + 7b) - 3y × (2a + 7b)
= (2a + 7b) × (2x - 3y)
14. a³c + b²d - b²c - a³d
c × (a³ - b²) - d (-b² + a³)
= (a³ - b²) × (c - d)
15. 12b³ - 15b² - 16b + 20
= 2(6b³ - 9b² - 8b + 10)