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

\(=4x^2-9y^2-4x^2+4x-1+9y^2-6y+1=4x-6y\)

Thay x = 1 ; y = -1 ta được : 

\(4+6=10\)

2x+\(\dfrac{1}{5}\) = 3y - \(\dfrac{2}{7}\) = 2x+3y -\(\dfrac{1}{6x}\) và 2x + 3y - z =50

có phải đề như này ko

bn viết rõ đề đi ạ:)

\(a,\left(2x-1\right)^2-\left(x-3\right)\left(x+3\right)-1969\\ =4x^2-4x+1-x^2+9-1969\\ =3x^2-4x-1959\)

\(b,\left(2x-3y\right)\left(2x+3y\right)-\left(2x-y\right)^2\\ =4x^2-9y^2-4x^2+4xy-y^2\\ =8y^2+4xy=4y\left(2y+x\right)\)

\(c,\left(x+3y\right)^2+\left(x+y\right)\left(x-y\right)+280\\ =x^2+6xy+9y^2+x^2-y^2+280\\ =2x^2+8y^2+6xy+280\)

a: \(\left(2x-1\right)^2-\left(x-3\right)\cdot\left(x+3\right)-1969\)

\(=4x^2-4x+1-x^2+9-1969\)

\(=3x^2-4x-1959\)

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

\(=4x^2-9y^2-4x^2+4xy-y^2\)

\(=-10y^2+4xy\)

a)\(\text{( 2 x − 1 )^2− ( x − 3 ) ( x + 3 ) − 1969}\)

\(\text{= 4x^2 − 4x + 1 − x^2 + 9 − 1969}\)

\(\text{=3x^2− 4 x − 1959}\)

b) \(\text{( 2 x − 3 y ) ( 2 x + 3 y ) − ( 2 x − y )^2}\)

=\(\text{= 4 x^2− 9 y^2− 4 x^2 + 4 x y − y^2}\)

\(\text{= -10 y^2+ 4 x y = -2 y ( 5 y -2 x )}\)

c)\(\text{( x + 3 y )^2 + ( x + y ) ( x − y ) + 280}\)

\(\text{= x^2 + 6 x y + 9 y^2 + x^2 − y^2 + 280}\)

\(\text{= 2 x^2 + 8 y^2 + 6 x y + 280}\)

(2x+3y)²+2(2x+3y)+1

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

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

(2x + 3y)\(^2\) + 2(2x + 3y) + 1

= (2x + 3y + 1)\(^2\)

AD HĐT : (a + b)\(^2\) = a\(^2\) + 2ab + b\(^2\)

\(\left(x+3y\right)^2-\left(2x-3y\right)^2-2x^2+12y^2\)

\(=x^2+2\cdot x\cdot3y+\left(3y\right)^2-\left[\left(2x\right)^2-2\cdot2x\cdot3y+\left(3y\right)^2\right]-2x^2+12y^2\)

\(=x^2+6xy+9y^2-4x^2+12xy-9y^2-2x^2+12y^2\)

\(=-5x^2+18xy+12y^2\)  

Điều kiện \(x\ne\pm3;y\ne-2\):

 \(P=\frac{2x+3y}{xy+2x-3y-6}-\frac{6-xy}{xy+2x+3y+6}-\frac{x^2+9}{x^2-9}.\)

=> \(P=\frac{2x+3y}{\left(y+2\right)\left(x-3\right)}-\frac{6-xy}{\left(y+2\right)\left(x+3\right)}-\frac{x^2+9}{\left(x-3\right)\left(x+3\right)}\)

\(P=\frac{\left(2x+3y\right)\left(x+3\right)-\left(6-xy\right)\left(x-3\right)-\left(x^2+9\right)\left(y+2\right)}{\left(y+2\right)\left(x-3\right)\left(x+3\right)}\)

\(P=\frac{2x^2+3xy+6x+9y-6x+x^2y+18-3xy-x^2y-9y-2x^2-18}{\left(y+2\right)\left(x-3\right)\left(x+3\right)}\)

\(P=\frac{0}{\left(y+2\right)\left(x-3\right)\left(x+3\right)}=0\)

=> P=0 (với mọi x khác 3, -3 và y khác -2)

a) \(\left(2x-3\right)^2=4x^2-12x+9\)

\(b.\left(x-3y\right)^2=x^2-6xy+9y^2\)

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

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

\(=-10y^2-4xy\)

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

d) \(\left(x+3y^2\right)^2\)

\(=x^2+6xy^2+9y^4\)

a, \(\left(3+2x\right)^2=9+12x+4x^2\)

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

c, \(\left(2x-3y\right)\left(2x+3y\right)=4x^2+6xy-6xy-9y^2=4x^2-9y^2\)

d, \(\left(2x+3y\right)^3=8x^3+36x^2y+54xy^2+27y^3\)

( 3 + 2x )² = 3² + 2.3.2x + ( 2x )² = 4x² + 12x + 9

( 3x - 2y )² = ( 3x )² - 2.3x.2y + ( 2y )² = 9x² - 12xy + 4y²

( 2x - 3y )( 2x + 3y ) = ( 2x )² - ( 3y )² = 4x² - 9y²

( 2x + 3y )³ = ( 2x )³ + 3( 2x )².3y + 3.2x.( 3y )² + ( 3y )³ = 8x³ + 36x²y + 54xy² + 27y³

Khai triển HĐT ?

a) \(\left(3+2x\right)^2=9+12x+4x^2\)

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

c) \(\left(2x-3y\right)\left(2x+3y\right)=4x^2-9y^2\)

d) \(\left(2x+3y\right)^3=8x^3+36x^2y+54xy^2+27y^3\)

a: \(\left(2x-3\right)^2=4x^2-12x+9\)

b: \(\left(x-3y\right)^2=x^2-6xy+9y^2\)

c: \(=4x^2-9y^2-4x^2-4xy-y^2\)

\(=-10y^2-4xy\)

d: \(\left(x+3y^2\right)^2=x^2+6xy^2+9y^4\)

a: \(\left(2x-3\right)^2=4x^2-12x+9\)

b: \(\left(x-3y\right)^2=x^2-6xy+9y^2\)

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

\(=4x^2-9y^2-4x^2-4xy-y^2=-8y^2-4xy\)

d: \(\left(x+3y^2\right)^2=x^2+6xy^2+9y^4\)