= (x+y)-(x-y).2a

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

=(x-y).2a

a x+ 2a(x-y)-y

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

=(x-y)(1+2a)

b x^2-(a+b)x+ab

=x^2-(xa+xb)+ab

=x^2-xa-xb+ab

=x(x-a)-b(x-a)

=(x-a)(x-b)

f x(y^2-z^2)+y(z^2-x^2)+z(x^2-y^2)

=xy^2-xz^2+yz^2-yx^2+zx^2-zy^2

=-xzy^2-xyz^2-zyx^2

=-xyz(y+z+x)

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

\(=xy^2-xz^2+yz^2-x^2y+zx^2-zy^2\)

\(=xy^2-xz^2+yz^2-x^2y+zx^2-zy^2-xyz+xyz\)

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

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

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

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

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

a,\(\left(a-b\right)\left(a+2b\right)-\left(b-a\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)

\(=\left(a-b\right)\left(a+2b\right)+\left(a-b\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)

\(=\left(a-b\right)\left(a+2b+2a-b-a-3b\right)\)

\(=\left(a-b\right)\left(2a-2b\right)\)

\(=\left(a-b\right)2\left(a-b\right)\)

\(=2\left(a-b\right)^2\)

b,\(\left(x+y\right)\left(2x-y\right)+\left(2x-y\right)\left(3x-y\right)-\left(y-2x\right)\)

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

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

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

c,\(x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\)

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

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

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

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

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

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

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

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

= ( a - b )[ ( a + 2b ) + ( 2a - b ) - ( a + 3b ) ]

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

= ( a - b )( 2a - 2b )

= 2( a - b )( a - b ) = 2( a - b )²

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

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

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

= ( 2x - y )( x + y + 3x - y + 1 )

= ( 2x - y )( 4x + 1 )

c) x²( y - z ) + y²( z - x ) + z²( x - y )

= x²y - x²z + y²z - y²x + z²( x - y )

= ( x²y - y²x ) - ( x²z - y²z ) + z²( x - y )

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

= xy( x - y ) - z( x - y )( x + y ) + z²( x - y )

= ( x - y )[ xy - z( x + y ) + z² ]

= ( x - y )( xy - zx - zy + z² )

= ( x - y )[ ( xy - zx ) - ( zy - z² ) ]

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

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

a,Từ giả thiết ta có

(x²+y²+z²)(x+y+z)²+(xy+yz+zx)²

=(x²+y²+z²)(x²+y²+z²+2xy+2yz+2zx)+(xy+yz+zx)²

Đặt x²+y²+z²=a

xy+yz+zx=b

=>(x²+y²+z²)(x²+y²+z²+2xy+2yz+2zx)+(xy+yz+zx)²

=a(a+2b)+b²

=a²+2ab+b²

=(a+b)²

=(x²+y²+z²+xy+yz+zx)²

câu b hơi dài mình gửi sau nhé

Ta có: 2(x^4+y^4+z^4)-(x^2+y^2+z^2)^2-2(x^2+y^2+z^2)(x+y+z)^2+(x+y+z)^4

Gọi x^4+y^4+z^4=a

x^2+y^2+z^2=b

x+y+z=c

=>2(x^4+y^4+z^4)-(x^2+y^2+z^2)^2-2(x^2+y^2+z^2)(x+y+z)^2+(x+y+z)^4=2a-b^2-2bc^2+c^4

=2a-2b^2+b^2-2bc^2+c^4

=2(a-b^2)+(b+c^2)^2

Ta có

2(a-b²)=2[x^4+y^4+z^4-(x^2+y^2+z^2)²]

=2[x^4+y^4+z^4-x^4-y^4-z^4-2x²y²-2y²z²-2z²x²]

=2.(-2)(x²y²+y²z²+z²x²)

=-4(x²y²+y²z²+z²x²)

Lại có

(b+c^2)^2

=[(x^2+y^2+z^2)+(x+y+z)²]²

=[(x^2+y^2+z^2)-(x^2+y^2+z^2)-2(xy+yz+zx)]²

=4(xy+yz+zx)²

=>2(a-b^2)+(b+c^2)^2

=-4(x²y²+y²z²+z²x²)+4(xy+yz+zx)²

=8xyz(x+y+z)

cauu a cua bn Đen đủi .....lm sai r

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

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

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

y(x+y)+yz(y+z)+xz(x+z)+2xyz 

= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz 

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

= xy(x + y) + z(x + y + z)(y + x) 

= (x + y)(xy + zx + zy + z²) 

= (x + y)[x(y + z) + z(y + z)] 

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

Monkey D.Luffy copy ở đâu mà hay z