Lời giải:

a.

$64x^2-24y^2=8(8x^2-3y^2)=8(\sqrt{8}x-\sqrt{3}y)(\sqrt{8}x+\sqrt{3}y)$

b.

$64x^3-27y^3=(4x)^3-(3y)^3=(4x-3y)(16x^2+12xy+9y^2)$

c.

$x^4-2x^3+x^2=(x^2-x)^2=[x(x-1)]^2=x^2(x-1)^2$

d.

$(x-y)^3+8y^3=(x-y)^3+(2y)^3=(x-y+2y)[(x-y)^2-2y(x-y)+(2y)^2]$

$=(x+y)(x^2-4xy+7y^2)$

a) \(64x^2-24y^2\)

\(=8\left(8x^2-3y^2\right)\)

b) \(64x^3-27y^3\)

\(=\left(4x\right)^3-\left(3y\right)^3\)

\(=\left(4x-3y\right)\left(16x^2+12xy+9y^2\right)\)

c) \(x^4-2x^3+x^2\)

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

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

d) \(\left(x-y\right)^3+8y^3\)

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

\(=\left(x+y\right)\left(x^2-4xy+7y^2\right)\)

x³ + 3x - 4 = x³ - x + 4x - 4

= x(x² - 1) + 4(x - 1)

= x(x + 1)(x - 1) + 4(x - 1)

= (x - 1) [ x(x + 1) + 4 ]

=(x - 1)(x² + x + 4)

\(x^3+3x-4\)

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

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

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

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

k mk nha

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

Đúng cho mình nha 

( x + y + z )³ - x³ - y³ - z³

= [ ( x + y + z )³ - x³ ] - ( y³ + z³ )

= ( x + y + z - x )[ ( x + y + z )² + ( x + y + z )x + x² ] - ( y + z )( y² - yz + z² )

= ( y + z )( 3x² + y² + z² + 2yz + 3zx + 3xy ) - ( y + z )( y² - yz + z² )

= ( y + z )( 3x² + y² + z² + 2yz + 3zx + 3xy - y² + yz - z² )

= ( y + z )( 3x² + 3yz + 3zx + 3xy )

= 3( y + z )( x² + yz + zx + xy )

= 3( y + z )[ ( x² + zx ) + ( xy + yz ) ]

= 3( y + z )[ x( x + z ) + y( x + z ) ]

= 3( y + z )( x + z )( x + y )

\(\left(x+y+z\right)^3-x^3-y^3-z^3\)

\(=\left[\left(x+y+z\right)^3-x^3\right]-\left(y^3+z^3\right)\)

\(=\left(x+y+z-x\right).\left[\left(x+y+z\right)^2+\left(x+y+z\right).x+x^2\right]-\left(y+z\right)\left(y^2-yz+z^2\right)\)

\(=\left(y+z\right).\left(x^2+y^2+z^2+2xy+2yz+2xz+x^2+yx+zx+x^2\right)-\left(y+z\right)\left(y^2-yz+z^2\right)\)

\(=\left(y+z\right).\left[x^2+y^2+z^2+2xy+2yz+2xz+x^2+yx+zx+x^2-\left(y^2-yz+z^2\right)\right]\)

\(=\left(y+z\right).\left(x^2+y^2+z^2+2xy+2yz+2xz+x^2+yx+zx+x^2-y^2+yz-z^2\right)\)

\(=\left(y+z\right).\left(3x^2+3xy+3yz+3xz\right)\)

\(=\left(y+z\right).\left[\left(3x^2+3xy\right)+\left(3yz+3xz\right)\right]\)

\(=\left(y+z\right).\left[3x.\left(x+y\right)+3z.\left(y+x\right)\right]\)

\(=\left(y+z\right).\left(x+y\right).\left(3x+3z\right)\)

\(=3.\left(y+z\right).\left(x+y\right).\left(x+z\right)\)

a: =64x^4+16x^2y^2+y^4-16x^2y^2

=(8x^2+y^2)^2-(4xy)^2

=(8x^2+y^2-4xy)(8x^2+y^2+4xy)

b: =x^8+2x^4+1-x^4

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

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

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

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

c: =(x+1)(x^2-x+1)+2x(x+1)

=(x+1)(x^2-x+1+2x)

=(x+1)(x^2+x+1)

d: =(x^2-1)(x^2+1)-2x(x^2-1)

=(x^2-1)(x^2-2x+1)

=(x-1)^2*(x-1)(x+1)

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

2x ( x - y ) - 10y ( x - y )

= ( x - y ) ( 2x - 10y )

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

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

2x ( x - y ) - 10y ( x - y )

= ( x - y ) ( 2x - 10y )

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

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

\(x^3-64x^2=x^2.\left(x-64\right)\)

\(x^3-64x^2=x^2.\left(x-64\right)\)

b: 6x^2-24y^2

=6(x^2-4y^2)

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

c: =(4x)^3-(3y)^3

=(4x-3y)(16x^2+12xy+9y^2)

d: x^4-2x^3-x^2

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