Question

Phân tích các đa thức sau thành nhân tử :

a) \(x^3-2x^2+x\)

b) \(2x^2+4x+2-2y^2\)

c) \(2xy-x^2-y^2+16\)

Answer 1

Bài giải:

a) x³ – 2x² + x = x(x² – 2x + 1) = x(x – 1)²

b) 2x² + 4x + 2 – 2y² = 2[(x² + 2x + 1) – y²]

= 2[(x + 1)² – y²]

= 2(x + 1 – y)(x + 1 + y)

c) 2xy – x² – y² + 16 = 16 – (x² – 2xy + y²) = 4² – (x – y)²

= (4 – x + y)(4 + x – y)

Answer 2

a) \(x^3 - 2x^2 + x\) \(= x(x^2 - 2x + 1)\)

\(= x (x - 1 )^2\)

b) \(2x^2 + 4x + 2 - 2y^2\) \(= 2(x^2 + 2x + 1 - y^2)\)

\(=2\left[\left(x^2+2x+1\right)-y^2\right]\)

\(=2\left[\left(x+1^2\right)-y^2\right]\)

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

c) \(2xy - x^2 - y^2 + 16\) \(= - (x^2 - 2xy + y^2 - 4^2)\)

\(= - [(x^2 - 2xy + y^2) - 4^2]\)

\(= - [(x-y)^2 - 4^2 ]\)

\(= - (x - y - 4) (x- y + 4)\)