Question

Phân tích thành nhân tử :

a) x^4 + 2x^3 + x^2                                                                                    b) x^3 - x + 3x^2y + 3xy^2 + y^3 - y

 c) 5x^2 - 10xy + 5y^2 - 20z^2                                                                   d) x^2 + 5x - 6

Answer 1

a) x^4 + 2x^3 + x^2                       

=x².(x²+2x+1)

=x².(x+1)²                                                             

b) x^3 - x + 3x^2y + 3xy^2 + y^3 - y

=(x³+3x²y+3xy²+y³)+(-x-y)

=(x+y)³-(x+y)

=(x+y)[(x+y)²-1]

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

 

 c) 5x^2 - 10xy + 5y^2 - 20z^2

=5.(x²-2xy+y²-4z²)

=5.[(x-y)²-4z²]

=5.(x-y-2z)(x-y+2z)                                                                  

d) x^2 + 5x - 6

=x²-x+6x-6

=x.(x-1)+6.(x-1)

=(x-1)(x+6)

Answer 2

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Answer 3

 

a) x^4 + 2x^3 + x^2                       

=x².(x²+2x+1)

=x².(x+1)²                                                             

b) x^3 - x + 3x^2y + 3xy^2 + y^3 - y

=(x³+3x²y+3xy²+y³)+(-x-y)

=(x+y)³-(x+y)

=(x+y)[(x+y)²-1]

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

 

 c) 5x^2 - 10xy + 5y^2 - 20z^2

=5.(x²-2xy+y²-4z²)

=5.[(x-y)²-4z²]

=5.(x-y-2z)(x-y+2z)                                                                  

d) x^2 + 5x - 6

=x²-x+6x-6

=x.(x-1)+6.(x-1)

=(x-1)(x+6)

Answer 4

\(x^2+5x-6\)

\(=x^2-x+6x-6\)

\(=x\left(x-1\right)+6\left(x-1\right)\)

\(=\left(x-1\right)\left(x+6\right)\)