Question

Phân tích các đa thức sau thành nhân tử 

a) \(8a^2xy-18b^2xy\)

b) \(32a^2b^2-4\)

c) \(x^2-49z^2-4xy+4y^2\)

d) \(3x^2+6x+3-3y^2\)

e) \(12x^2y-12y^3+36xy+27y\)

Answer 1

a) \(8a^2xy-18b^2xy=2xy\left(4a^2-9b^2\right)=2xy\left(2a-3b\right)\left(2a+3b\right)\)

b) \(32a^2b^2-4=4\left(8a^2b^2-1\right)\)

c) \(x^2-49z^2-4xy+4y^2=\left(x^2-4xy+4y^2\right)-49z^2\)

\(=\left(x-2y\right)^2-\left(7z\right)^2=\left(x-2y+7z\right)\left(x-2y-7z\right)\)

d) \(3x^2+6x+3-3y^2=3\left(x^2+2x+1-y^2\right)=3.\left[\left(x+1\right)^2-y^2\right]\)

\(=3\left(x-y+1\right)\left(x+y+1\right)\)

e) \(12x^2y-12y^3+36xy+27y=3y\left(4x^2-4y^2+12x+9\right)\)

\(=3y\left[\left(4x^2+12x+9\right)-4y^2\right]=3y\left[\left(2x+3\right)^2-\left(2y\right)^2\right]\)

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

Answer 2

a) 8a²xy - 18b²xy 

= 2xy( 4a² - 9b² )

= 2xy( [ ( 2a )² - ( 3b )² ]

= 2xy( 2a - 3b )( 2a + 3b )

b) 32a²b² - 4

= 4( 8a²b² - 1 )

c) x² - 49z² - 4xy + 4y²

= ( x² - 4xy + 4y² ) - 49z²

= ( x - 2y )² - ( 7z )²

= ( x - 2y - 7z )( x - 2y + 7z )

d) 3x² + 6x + 3 - 3y²

= 3( x² + 2x + 1 - y² )

= 3[ ( x² + 2x + 1 ) - y² ]

= 3[ ( x + 1 )² - y² ]

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

e) 12x²y - 12y³ + 36xy + 27y

= 3y( 4x² - 4y² + 12x + 9 )

= 3y[ ( 4x² + 12x + 9 ) - 4y² ]

= 3y[ ( 2x + 3 )² - ( 2y )² ]

= 3y( 2x - 2y + 3 )( 2x + 2y + 3 )