\(x^2-4xy+4y^2-z^2+4zt-4t^2\)

\(=x^2-2xy-2xy+4y^2-\left(z^2-2zt-2zt+4t^2\right)\)

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

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

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a) \(9\left(2x-3\right)^2-4\left(x+1\right)^2\)

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

\(=\left(6x-9-2x-2\right)\left(6x-9+2x+2\right)\)

\(=\left(4x-11\right)\left(8x-7\right)\)

b) \(\left(x^2+4y^2-20\right)-16\left(xy-4\right)^2\)

\(=\left[\left(x^2-4xy+4y^2\right)-4\right]\left[\left(x^2+4xy+4y^2\right)-36\right]\)

\(=\left[\left(x-2y\right)^2-4\right]\left[\left(x+2y\right)^2-36\right]\)

\(=\left(x-2y-2\right)\left(x-2y+2\right)\left(x+2y-6\right)\left(x+2y+6\right)\)

a. 9 ( 2x - 3 )² - 4 ( x + 1 )²

= [ 3 ( 2x - 3 ) ]² - [ 2 ( x + 1 ) ]²

= [ 3 ( 2x - 3 ) - 2 ( x + 1 ) ] [ 3 ( 2x - 3 ) + 2 ( x + 1 ) ]

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

= ( 4x - 11 ) ( 8x - 7 )

b. ( x² + 4y² - 20 )² - 16 ( xy - 4 )²

= ( x² + 4y² - 20 )² - [ 4 ( xy - 4 ) ]²

= [ x² + 4y² - 20 - 4 ( xy - 4 ) ] [ x² + 4y² - 20 + 4 ( xy - 4 ) ]

= ( x² + 4y² - 20 - 4xy + 16 ) ( x² + 4y² - 20 + 4xy - 16 )

 = ( x² + 4y² - 4xy - 4 ) ( x² + 4y² + 4xy - 36 )

= [ ( x - 2y )² - 2² ] [ ( x + 2y )² - 6² ]

= ( x - 2y - 2 ) ( x - 2y + 2 ) ( x + 2y - 6 ) ( x + 2y + 6 )

b)  \(64x^3+1=\left(4x+1\right)\left(16x^2-4x+1\right)\)\

c) \(x^3y^6z^9-125=\left(xy^2z^3-5\right)\left(x^2y^4z^6+5xy^2z+25\right)\)

d)  \(27x^6-8x^3=x^3\left(27x^3-8\right)=x^3\left(3x-2\right)\left(9x^2+6x+4\right)\)

e)  \(x^6-y^6=\left(x^3-y^3\right)\left(x^3+y^3\right)=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)

64x³ + 1

= ( 4x )³  +  1

= ( 4x + 1 ) ( 16x² - 4x + 1 )

Hằng đẳng thức 6 : A³ + B³

27x⁶ - 8x³

= ( 3x²)³ + ( 2x )³

= ( 3x + 2x ) ( 9x² - 6x + 4x² )

HĐT 6

x⁶ - y⁶

= ( x² )³ - ( y² )³

= ( x² - y² ) ( x⁴ + x²y² + y⁴ )

HĐT 7 : A³ - B³

x³y⁶z⁹ + 1

= ( xy²z³)³ + 1

= ( xy²z³ + 1 ) ( x²y⁴z⁶ + zy²z³ + 1 )

HĐT 6