Phân tích đa thức thành nhân tử:

a) 3x² – 6xy + 3y² – 12;

b) 4x² – 4x + 1 – 9y²;

c) 9x² – 6x + 1 – 16y².

Lời giải

a) 3x² – 6xy + 3y² – 12

= 3(x² – 2xy + y² – 4)

= 3[(x – y)² – 2²]

= 3(x – y + 2)(x – y – 2).

b) 4x² – 4x + 1 – 9y²

= (2x – 1)² – (3y)²

= (2x – 1 – 3y)(2x – 1 + 3y).

c) 9x² – 6x + 1 – 16y²

= (3x – 1)² – (4y)²

= (3x – 1 – 4y)(3x – 1 + 4y).