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

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

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

\(C=\left(x+1\right)^3-\left(x-2\right)^3=\left(x^3+3x^2+3x+1\right)-\left(x^3-6x^2+12x-8\right)\)

\(=x^3+3x^2+3x+1-x^3+6x^2-12x+8=9x^2-9x+9=9\left(x^2-x+1\right)\)

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

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

\(=x^2+4xy+4y^2+2x^2-8y^2+2y-x=3x^2-4y^2+4xy+2y-x\)

\(G=\left(2x+1\right)^3-\left(2x-1\right)=8x^3+12x^2+6x+1-2x+1=8x^3+12x^2+4x+2\)

\(=2\left(4x^3+6x^2+2x+1\right)=2\left(4x\left(x+1\right)^2+1\right)\)

lồn là vịt

\(\left(\dfrac{x}{x+2y}-\dfrac{x+2y}{2y}\right)\left(\dfrac{x}{x-2y}-1+\dfrac{8y^3}{8y^3-x^3}\right)=\dfrac{2xy-\left(x+2y\right)^2}{2y\left(x+2y\right)}\left(\dfrac{2y}{x-2y}+\dfrac{8y^3}{\left(2y-x\right)\left(4y^2+2yx+x^2\right)}\right)=\dfrac{-\left(x^2+2xy+4y^2\right)}{2y\left(x+2y\right)}\cdot\dfrac{2y\left(4y^2+2yx+x^2\right)-8y^3}{\left(x-2y\right)\left(x^2+2xy+4y^2\right)}=\dfrac{-\left(x^2+2xy+4y^2\right)2y\left(4y^2+2xy+x^2-4y^2\right)}{2y\left(x+2y\right)\left(x-2y\right)\left(x^2+2x+4y^2\right)}=\dfrac{-\left(x^2+2xy\right)}{\left(x+2y\right)\left(x-2y\right)}=\dfrac{x}{2y-x}\)

A = ( x - 2 )² - ( 2x + 1 )² 

A = x² - 4x + 4 - 4x² + 4x + 1 

A = - 3x² + 5 

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

B = x² - 4xy + 4y² - ( 2xy + x² - 4y² - 2xy ) 

B = x² - 4xy + 4y² - 2xy - x² + 4y² + 2xy 

B = 8y² - 4xy 

Rút gọn hả bạn ?

( 3x - 1 )² - 9( x - 1 )( x + 1 )

= 9x² - 6x + 1 - 9( x² - 1 )

= 9x² - 6x + 1 - 9x² + 9

= 10 - 6x

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

= 4x² - 9 - ( 4x² - 4x + 1 ) - x + 1

= 4x² - x - 8 - 4x² + 4x - 1

= 3x - 9

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

= [ ( x + 2y ) + ( x - 2y ) ]²

= [ x + 2y + x - 2y ]²

= ( 2x )² = 4x²

m: (x-y)(x^2-2xy+y^2)

=(x-y)*(x-y)^2

=(x-y)^3

=x^3-3x^2y+3xy^2-y^3

n: =-(x^3+x^2y-x-x^2y-xy^2+y)

=-x^3+x+xy^2-y

o: =-(x^3+x^2y^2-x^2-2xy-2y^3+2y)

=-x^3-x^2y^2+x^2+2xy+2y^3-2y

p: (1/2x-1)(2x-3)

=1/2x*2x-1/2x*3-2x+3

=x^2-3/2x-2x+3

=x^2-7/2x+3

q: (x-1/2y)(x-1/2y)

=(x-1/2y)^2

=x^2-xy+1/4y^2

r: (x^2-2x+3)(1/2x-5)

=1/2x^3-5x^2-x^2+10x+3/2x-15

=1/2x^3-6x^2+11,5x-15

bạn chịu khó suy nghĩ chút sẽ ra bài này dễ mà

có kq

đố là x=1/12;y=1/24;z=1/36

\(VT=\dfrac{2y+3z+5}{1+x}+1+\dfrac{3z+x+5}{2y+1}+1+\dfrac{x+2y+5}{1+3z}+1-3\)

\(VT=\dfrac{x+2y+3z+6}{1+x}+\dfrac{x+2y+3z+6}{1+2y}+\dfrac{x+2y+3z+6}{1+3z}-3\)

\(VT=24\left(\dfrac{1}{1+x}+\dfrac{1}{1+2y}+\dfrac{1}{1+3z}\right)-3\ge\dfrac{24.9}{1+x+1+2y+1+3z}-3=\dfrac{216}{21}-3=\dfrac{51}{7}\)