a: \(=\left(x^4-4\right)+5x\left(x^2+2\right)\)

\(=\left(x^2+2\right)\left(x^2+5x-2\right)\)

b: \(x^8+x+1\)

\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)

\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)

c: \(x^5+x^4+1\)

\(=x^5+x^4+x^3-x^3-x^2-x+x^2+x+1\)

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

a) \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-8\)

\(=\left[\left(x+1\right)\left(x+4\right)\right]\left[\left(x+2\right)\left(x+3\right)\right]-8\)

\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-8\)

\(=\left(x^2+5x+5\right)^2-1-8\)

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

\(=\left(x^2+5x+2\right)\left(x^2+5x+8\right)\)

b) \(xy\left(x-y\right)+yz\left(y-z\right)+zx\left(z-x\right)\)

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

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

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

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

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

a) ( x + 1 )( x + 2 )( x + 3 )( x + 4 ) - 8

= [ ( x + 1 )( x + 4 ) ][ ( x + 2 )( x + 3 ) ] - 8

= ( x² + 5x + 4 )( x² + 5x + 6 ) - 8

Đặt t = x² + 5x + 5

bthuc ⇔ ( t - 1 )( t + 1 ) - 8

           = t² - 1 - 8

           = t² - 9

           = ( t - 3 )( t + 3 )

           = ( x² + 5x + 5 - 3 )( x² + 5x + 5 + 3 )

           = ( x² + 5x + 2 )( x² + 5x + 8 )

b) xy( x - y ) + yz( y - z ) + zx( z - x )

= x²y - xy² + y²z - yz² + zx( z - x )

= ( y²z - xy² ) - ( yz² - x²y ) + zx( z - x )

= y²( z - x ) - y( z² - x² ) + zx( z - x )

= ( z - x )( y² + zx ) - y( z - x )( z + x )

= ( z - x )( y² + zx - yz - yx )

= ( z - x )[ ( y² - yx ) - ( yz - zx ) ]

= ( z - x )[ y( y - x ) - z( y - x ) ]

= ( z - x )( y - x )( y - z )

a: A=y(x-4)-5(x-4)

=(x-4)(y-5)

Khi x=14 và y=5,5 thì A=(14-4)(5,5-5)=0,5*10=5

b: \(B=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\)

Khi x=5,2 và y=4,8 thì B=(5,2+4,8)(5,2-5)

=0,2*10=2

d: Khi x=5,75 và y=4,25 thì

D=5,75^3-5,75^2*4,25+4,25^3

=8087/64

A ) xy(z+y)+yz(y+z)+zx(z+x)

=y.[x(z+y)+z(y+z)]+zx(z+x)

=y.(xz+xy+zy+z²)+zx(z+x)

=y.(xz+z²+xy+zy)+zx(z+x)

=y.[z.(z+x)+y.(z+x)]+zx(z+x)

=y.(z+x)(z+y)+zx(z+x)

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

=(z+x)(yz+y²+zx)

B )xy(x+y)-yz(y+z)-zx(z-x)

=y.[x(x+y)-z(y+z)]-zx(z-x)

=y.(x²+xy-zy-z²)-zx(z-x)

=y.(x²-z²+xy-zy)-zx(z-x)

=y.[(x+z)(x-z)+y.(x-z)]-zx(z-x)

=y.(x-z)(x+z+y)+zx(x-z)

=(x-z)[y(x+z+y)+zx]

=(x-z)(yx+yz+y²+zx)

=(x-z)(yx+zx+yz+y²)

=(x-z)[x.(y+z)+y.(y+z)]

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

b. \(\text{ xy(x+y)-yz(y+z)-xz(z-x) =xy(x+y+z-z)+yz(y+z)+xz(x-z) =xy(x-z)+xy(y+z)+yz(y+z)+xz(x-z) =(x+y)(y+z)(x-z) }\)

a: \(2x^2+3xy-14y^2\)

\(=2x^2+7xy-4xy-14y^2\)

\(=\left(2x^2+7xy\right)-\left(4xy+14y^2\right)\)

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

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

b: \(\left(x-7\right)\left(x-5\right)\left(x-3\right)\left(x-1\right)+7\)

\(=\left(x-7\right)\left(x-1\right)\left(x-5\right)\left(x-3\right)+7\)

\(=\left(x^2-8x+7\right)\left(x^2-8x+15\right)+7\)

\(=\left(x^2-8x\right)^2+15\left(x^2-8x\right)+7\left(x^2-8x\right)+105+7\)

\(=\left(x^2-8x\right)^2+22\left(x^2-8x\right)+112\)

\(=\left(x^2-8x\right)^2+8\left(x^2-8x\right)+14\left(x^2-8x\right)+112\)

\(=\left(x^2-8x\right)\left(x^2-8x+8\right)+14\left(x^2-8x+8\right)\)

\(=\left(x^2-8x+8\right)\left(x^2-8x+14\right)\)

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

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

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

\(=\left(x-3+6x-2\right)\left(x-3-3x+1\right)\)

\(=\left(7x-5\right)\left(-2x-2\right)\)

\(=-2\left(x+1\right)\left(7x-5\right)\)

d: \(xy\left(x-y\right)+yz\left(y-z\right)+zx\left(z-x\right)\)

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

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

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

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

\(=\left(x-z\right)\left(xy+zy-y^2-xz\right)\)

\(=\left(x-z\right)\left[\left(xy-y^2\right)+\left(zy-zx\right)\right]\)

\(=\left(x-z\right)\left[y\cdot\left(x-y\right)-z\left(x-y\right)\right]\)

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

a: A=yx-4y-5x+20

=y(x-4)-5(x-4)

=(x-4)(y-5)

Khi x=14 và y=5,5 thì A=(14-4)(5,5-5)=0,5*10=5

b: \(B=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\)

Khi x=5,2 và y=4,8 thì B=(5,2+4,8)(5,2-5)

=0,2*10=2

d: Khi x=5,75 và y=4,25 thì

D=5,75^3-5,75^2*4,25+4,25^3

=8087/64

c: \(D=xyz-xy-yz-xz+x+y+z-1\)

=xy(z-1)-yz+y-xz+z+x-1

=xy(z-1)-y(z-1)-z(x-1)+(x-1)

=(z-1)(xy-y)-(x-1)(z-1)

=(z-1)(xy-y-1)

=(11-1)(9*10-10-1)

=10*79=790

1) \(4x^2-7x-2=4x^2-8x+x-2=\left(4x^2-8x\right)+\left(x-2\right)\)

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

2) \(4x^2+5x-6=4x^2+8x-3x-6=\left(4x^2+8x\right)-\left(3x+6\right)\)

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

3) \(5x^2-18x-8=5x^2-20x+2x-8=\left(5x^2-20x\right)+\left(2x-8\right)\)

\(=5x\left(x-4\right)+2\left(x-4\right)=\left(x-4\right)\left(5x+2\right)\)

4) \(xy\left(x+y\right)-yz\left(y+z\right)+xz\left(x-z\right)\)

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

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

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

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

\(=xy\left(x+y\right)+\left(zx-zy\right)\left(x+y\right)-z^2\left(x+y\right)\)

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

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

1) 4x² - 7x - 2 = 4x² - 8x + x - 2 = 4x( x - 2 ) + ( x - 2 ) = ( x - 2 )( 4x + 1 )

2) 4x² + 5x - 6 = 4x² - 8x + 3x - 6 = 4x( x - 2 ) + 3( x - 2 ) = ( x - 2 )( 4x + 3 )

3) 5x² - 18x - 8 = 5x² - 20x + 2x - 8 = 5x( x - 4 ) + 2( x - 4 ) = ( x - 4 )( 5x + 2 )

4) xy( x + y ) - yz( y + z ) + xz( x - z )

= x²y + xy² - y²z - yz² + xz( x - z )

= ( x²y - yz² ) + ( xy² - y²z ) + xz( x - z )

= y( x² - z² ) + y²( x - z ) + xz( x - z )

= y( x - z )( x + z ) + y²( x - z ) + xz( x - z )

= ( x - z )[ y( x + z ) + y² + xz ]

= ( x - z )( xy + yz + y² + xz )

= ( x - z )[ ( xy + y² ) + ( xz + yz ) ]

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

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

5) xy( x + y ) + yz + xz( x + z ) + 2xyz ( đề có thiếu không vậy .-. )

\(4x^2-7x-2=\left(4x^2-8x\right)+\left(x-2\right)=4x\left(x-2\right)+\left(x-2\right)=\left(4x-1\right)\left(x-2\right)\)

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

\(=5x^2-18x-8=5x^2-20x+2x-8=5x\left(x-4\right)+2\left(x-4\right)=\left(5x+2\right)\left(x-4\right)\)

\(5=\left(x+y\right)\left(y+z\right)\left(z+x\right)\)

\(a,=\left(xy-1-x-y\right)\left(xy-1+x+y\right)\\ b,Sửa:a^3+2a^2+2a+1\\ =a^3+a^2+a^2+a+a+1=\left(a+1\right)\left(a^2+a+1\right)\\ c,=1-4a^2-a\left(a^2-4\right)=1-4a^2-a^3+4a\\ =\left(1-a\right)\left(1+a+a^2\right)+4a\left(1-a\right)\\ =\left(1-a\right)\left(1+5a+a^2\right)\\ d,=\left(a^2-a^2b^2\right)+\left(b^2-b\right)+\left(ab-a\right)\\ =a^2\left(1-b\right)\left(1+b\right)+b\left(b-1\right)+a\left(b-1\right)\\ =\left(b-1\right)\left(-a^2-ab+b+a\right)\\ =\left(b-1\right)\left(b-1\right)\left(a+b\right)\left(1-a\right)\)

\(e,=x^2y+xy^2-yz\left(y+z\right)+x^2z-xz^2\\ =\left(x^2y+x^2z\right)+\left(xy^2-xz^2\right)-yz\left(y+z\right)\\ =x^2\left(y+z\right)+x\left(y-z\right)\left(y+z\right)-yz\left(y+z\right)\\ =\left(y+z\right)\left(x^2+xy-xz-yz\right)\\ =\left(y+z\right)\left(x+y\right)\left(x-z\right)\)

\(f,=xyz-xy-yz-xz+x+y+z-1\\ =xy\left(z-1\right)-y\left(z-1\right)-x\left(z-1\right)+\left(x-1\right)\\ =\left(z-1\right)\left(xy-y-x+1\right)=\left(z-1\right)\left(x-1\right)\left(y-1\right)\)