Bài 1: Phân tích các đa thức sau thành nhân tử:
1) 2x² - 2y² - 3x + 3y
= 2(x² - y²) - 3(x - y)
= 2(x - y)(x + y) - 3(x - y)
= (x - y)(2x + 2y - 3)

2) 6a² - 12ab + 6b² - 24c²
= 6(a² - 2ab + b²) - 24c²
= 6(a - b)² - 24c²
= 6[(a - b)² - 4c²]
= 6(a - b - 2c)(a - b + 2c)

3) 2a² + 4ab + 2b² - 2ac - 2bc
= 2(a² + 2ab + b² - ac - bc)
= 2[(a + b)² - c(a + b)]
= 2(a + b)(a + b - c)

4) x²y - x³ - 16y + 16x
= x²(y - x) - 16(y - x)
= (y - x)(x² - 16)
= (y - x)(x - 4)(x + 4)

5) 9x² - 25 + (3x + 7)(5 - 3x)
= (3x)² - 5² + (3x + 7)(5 - 3x)
= (3x - 5)(3x + 5) + (3x + 7)(5 - 3x)
= (3x - 5)(3x + 5 - 3x - 7)
= (3x - 5)(-2)
= -2(3x - 5)

6) 3(x + 4) - 3x² - 12x
= 3(x + 4) - 3x(x + 4)
= (x + 4)(3 - 3x)
= 3(x + 4)(1 - x)

7) 36x³y + 0.49yz³
= (6xy)² + (0.7z)²
= (6xy + 0.7z)(6xy - 0.7z)

8) 5x + 5y - x² - xy
= 5(x + y) - x(x + y)
= (x + y)(5 - x)

9) 2x² - 50 + y² + 2xy
= (x² + 2xy + y²) - 50
= (x + y)² - 5²
= (x + y - 5)(x + y + 5)

10) x² - 2x - 4y - 4y
= (x² - 2x) - (4y + 4y)
= x(x - 2) - 8y

11) x²(x - 3) + 25(3 - x)
= x²(x - 3) - 25(x - 3)
= (x - 3)(x² - 25)
= (x - 3)(x - 5)(x + 5)

12) 7x³ + 7x²y - 4x - 4y
= 7x²(x + y) - 4(x + y)
= (x + y)(7x² - 4)

13) 6x² - 6y² - 12x + 12y
= 6(x² - y²) - 12(x - y)
= 6(x - y)(x + y) - 12(x - y)
= 6(x - y)(x + y - 2)

14) 2x⁴ - 8x³ + 8x²
= 2x²(x² - 4x + 4)
= 2x²(x - 2)²