\(a^3-b^3+2b-2a=\left(a-b\right)\left(a^2+ab+b^2\right)-2\left(a-b\right)=\left(a-b\right)\left(a^2+ab+b^2-2\right)\)

phân tích đa thức thành nhân tử:

a,x^3-4x^2+4x-xy^2

b,x^3 -4x^2 +121x-27

c,3x^2 -7x -10

d,5x^3 -5x^2y -10x^2 +10xy

a) x3 - 4x2 + 4x - xy2

= x(x2 - 4x + 4 - y2)

= \(x\left [ (x - 2)^{2} - y^{2}\right ]\)

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

c) 3x2 - 7x - 10

= 3x2 + 3x - 10x - 10

= 3x(x + 1) - 10(x + 1)

= (x + 1)(3x - 10)

d) 5x3 - 5x2y - 10x2 + 10xy

= 5x(x2 - xy - 2x + 2y)

= \(5x\left [ x(x - y) - 2(x - y) \right ]\)

= 5x(x - y)(x - 2)

b) sửa đề: x3 - 4x2 + 12x - 27

= x3 - 27 - 4x2 + 12x

= (x - 3)(x2 + 3x + 9) - 4x(x - 3)

= (x - 3)(x2 + 3x - 4x + 9)

= (x - 3)(x2 - x + 9)

phân tích đa thức thành nhân tử

x4+2015x2+2014x+2015

\(x^4+2015x^2+2014x+2015\)

\(=\left(x^4-x^3+2015x^2\right)+\left(x^3-x^2+2015x\right)+\left(x^2-x+2015\right)\)

\(=\left(x^2-x+2015\right)\left(x^2+x+1\right)\)

Phân tích các đa thức sau thành nhân tử:

a, x4 + 1996.x2 + 1995.x + 1996

b, x4 + 1997.x2 + 1996.x + 1997

a)

\(x^4+1996x^2+1995x+1996\)

\(=\left(x^4-x\right)+\left(1996x^2+1996x+1996\right)\)

\(=x\left(x^3-1\right)+1996\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+1996\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left[x\left(x-1\right)+1996\right]\)

\(=\left(x^2+x+1\right)\left(x^2-x+1996\right)\)

b)

\(x^4+1997x^2+1996x+1997\)

\(=\left(x^4-x\right)+\left(1997x^2+1997x+1997\right)\)

\(=x\left(x^3-1\right)+1997\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+1997\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left[x\left(x-1\right)+1997\right]\)

\(=\left(x^2+x+1\right)\left(x^2-x+1997\right)\)

phân tích đa thức thành nhân tử

x^5 - 3x^4 + 3x^3 - x^2

3y^2 - 3z^2 + 3x^2

a, \(x^5-3x^4+3x^3-x^2\)

= \((x^5-x^2)-(3x^4-3x^3)\)

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

= \(x^2(x-1)\left(x^2+x+1\right)-3x^3(x-1)\)

= \((x-1)\left(x^4+x^3+x^2\right)-3x^3(x-1)\)

= \((x-1)\left(x^4+x^3+x^2-3x^3\right)\)

= \((x-1)\left(x^4-2x^3+x^2\right)\)

Phân tích đa thức sau thành nhân tử:

a) x^2-7x-30

b) x^2-x-6

c) x^2+x-30

2x2 + x - 6
pt thành nhân tử

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

\(=2x^2+4x-3x-6\)

\(=\left(2x^2+4x\right)-\left(3x+6\right)\)

\(=2x\left(x+2\right)-3\left(x+2\right)\)

\(=\left(x+2\right)\left(2x-3\right)\)

a) \(x^2-7x-30\)

\(=x^2+10x-3x-30\)

\(=x\left(x+10\right)-3\left(x+10\right)\)

\(=\left(x+10\right)\left(x-3\right)\)

b) \(x^2-x-6\)

\(=x^2+3x-2x-6\)

\(=x\left(x+3\right)-2\left(x+3\right)\)

\(=\left(x+3\right)\left(x-2\right)\)

c) \(x^2+x-30\)

\(=x^2+6x-5x-30\)

\(=x\left(x+6\right)-5\left(x+6\right)\)

\(=\left(x+6\right)\left(x-5\right)\)