Question

phân tích đa thức thành nhân tử:

a, -y² + 2xy - x² +3x - 3y

b, x³ - 2x² - x +2

c, x² (x+1) - 2x(x +1) + x+1

d, a² + b² +2a - 2b - 2ab

e, 4x² - 8x + 3

f, 25 -16x²

Answer 1

a) -y² + 2xy - x² + 3x - 3y

= (3x - 3y) - (x² - 2xy + y²)

= 3(x - y) - (x - y)²

= (x - y)(3 - x + y)

b) x³ - 2x² - x + 2

= (x³ - x) - (2x² - 2)

= x(x² - 1) - 2(x² - 1)

= (x² - 1)(x - 2)

= (x - 2)(x - 1)(x + 1)

c) x²(x + 1) - 2x(x + 1) + x + 1

= (x + 1)(x² - 2x + 1)

= (x + 1)(x - 1)²

d) a² + b² + 2a - 2b - 2ab

= (a² - 2ab + b²) + (2a - 2b)

= (a - b)² + 2(a - b)

= (a - b)(a - b + 2)

e) 4x² - 8x + 3

= (4x² - 2x) - (6x - 3)

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

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

f) 25 - 16x²

= 5² - (4x)²

= (5 - 4x)(5 + 4x)

Answer 2

a, -y² + 2xy - x² + 3x - 3y

= - (x² - 2xy + y²) + 3(x - y)

= - (x - y)² + 3(x - y)

= (x - y) (3 - x + y)

b, x³ - 2x² - x + 2

= x² (x - 2) - (x - 2)

= (x - 2)(x² - 1)

= (x - 2)(x - 1)(x + 1)

c, x² (x + 1) - 2x(x + 1) + x + 1

= x² (x + 1) - 2x(x + 1) + (x + 1)

= (x + 1)(x² - 2x + 1)

= (x + 1)(x - 1)²

d, a² + b² + 2a - 2b - 2ab

= (a² - 2ab + b² )+ (2a - 2b)

= (a - b)² + 2(a - b)

= (a - b)( a - b + 2)

e, 4x² - 8x + 3

= 4x² - 2x - 6x + 3

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

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

f, 25 - 16x²

= 5² - (4x)²

= (5 - 4x)(5 + 4x)

Chúc bạn học tốt!