Question

phân tích tành nhân tử

a, x^3 + y^3 +z^3- 3xyz

b, (x-1)(x - 2)(x -3)(x-4) - 3

Answer 1

x³ + y³ + z³ - 3xyz

= (x³ + 3x²y + 3xy² + y³) + z³ - (3x²y + 3xy² + 3xyz)

= (x + y)³ + z³ - 3xy(x + y + z)

= (x + y + z)[(x + y)² - z(x + y) + z²] - 3xy(x + y + z)

= ( x + y + z)(x² + 2xy + y² - xz - zy + z² - 3xy)

= (x + y + z)(x² + y² + z² - xy - yz - xz)

b. (x - 1)(x - 2)(x - 3)(x - 4) - 3

= (x - 1)(x - 4)(x - 2)(x - 3) - 3

= (x² - 5x + 4)(x² - 5x + 6) - 3

Đặt t = x² - 5x + 4

=> Đa thức

<=> t.(t + 2) - 3

= t² + 2t - 3

= t² + 3t - t - 3

= t.(t + 3) - (t + 3)

= (t + 3)(t + 1) (1)

Thay t = x² - 5x + 4 vào (1):

=> (x - 1)(x - 2)(x - 3)(x - 4) - 3

= (x² - 5x + 4 + 3)(x² - 5x + 4 + 1)

= (x² - 5x + 7)(x² - 5x + 5)