Question

BT: Phân tích các đa thức sau thành nhân tử

a, 3x.( x-1 )² - ( 1-x )³

b, 4x² - 2xy

c, 3x²y² - 5x⁴y⁴ + 7xy

d, ( x-3 )² - 2.( x-3 )

e, 3x². ( x-1 ) - ( 1-x )²

f, 2x^m-2.y - x^m+2.y

g, ( 2x - 2 )² - 2.(2x - 2 )

h, 3.(x-2)³ - 7y.( 3-x )

k, 3y.(x+3) + 5.( 3+x )

Answer 1

a, \(3x\left(x-1\right)^2-\left(1-x\right)^3\)

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

= \(3x^4-6x^2+3x-1+3x-3x^3+x^3\)

= \(3x^4-2x^3-6x^2-1\)

b, \(4x^2-2xy\)

= \(2x\left(2x-y\right)\)

c, \(3x^2y^2-5x^4y^4+7xy\)

= \(xy\left(3xy-5x^2y^2+7\right)\)

d, \(\left(x-3\right)^2-2\left(x-3\right)\)

= \(x^2-6x+9-2x+6\)

= \(x^2-8x+15\)

e,\(3x^2\left(x-1\right)-\left(1-x\right)^2\)

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

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