\(A=x^3-y^3-9xy=\left(x-y\right)\left(x^2+xy+y^2\right)-9xy=3\left(x^2+xy+y^2\right)-9xy\) (vì x - y = 3)

\(=3x^2+3xy+3y^2-9xy=3x^2-6xy+3y^2=3\left(x^2-2xy+y^2\right)=3\left(x-y\right)^2=27\)(vì x - y = 3)

a, Thay x = -2 ; y = 3 ta được 

\(A=\dfrac{4\left(-2\right)-5.3}{8\left(-2\right)-7.3}=\dfrac{-8-15}{-16-21}=\dfrac{23}{37}\)

b, Ta có \(\dfrac{x}{y}=\dfrac{5}{4}\Rightarrow\dfrac{x}{5}=\dfrac{y}{4}=k\Rightarrow x=5k;y=4k\)

Thay vào ta được \(A=\dfrac{4.5k-5.4k}{8.5k-7.4k}=\dfrac{0}{40k-28k}=0\)

ĐK: \(3x\ne\pm y;x\ne0\)

A = \(\dfrac{3x}{3x+y}-\dfrac{x}{3x-y}+\dfrac{2x}{\left(3x-y\right)\left(3x+y\right)}\)

= \(\dfrac{3x\left(3x-y\right)-x\left(3x+y\right)+2x}{\left(3x-y\right)\left(3x+y\right)}=\dfrac{6x^2-4xy+2x}{\left(3x-y\right)\left(3x+y\right)}=\dfrac{2x\left(3x-2y+1\right)}{\left(3x-y\right)\left(3x+y\right)}\)

Thay x = 1; y=2, ta có:

A = \(\dfrac{2.1\left(3.1-2.2+1\right)}{\left(3.1-2\right)\left(3.1+2\right)}=0\)

\(A=\dfrac{2x^2\left(3x-4y+2\right)}{x\left(3x+y\right)\left(3x-y\right)}=\dfrac{2x\left(3x-4y+2\right)}{\left(3x+y\right)\left(3x-y\right)}\\ A=\dfrac{2\left(3-8+2\right)}{\left(3+2\right)\left(3-2\right)}=\dfrac{2\left(-3\right)}{5}=\dfrac{-6}{5}\)

b) \(x^3-y^3-3xy\)

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

\(=\left(x-y\right)\left[\left(x+y\right)^2-2xy+xy\right]-3xy\)

\(=\left(x-y\right)\left(1-xy\right)-3xy\)

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

a)a+b+c=9

=>(a+b+c)²=81

=>a²+b²+c²+2ab+2bc+2ca=81

Từ a²+b²+c²=141=>2ab+2bc+2ca=81-141=-60

=>2(ab+bc+ca)=-60=>ab+bc+ca=-30

b)x+y=1

=>(x+y)³=1

=>x³+3x²y+3xy²+y³=1

=>x³+y³+3xy(x+y)=1

=>x³+y³+3xy=1(Do x+y=1)

c)a³-3ab+2c=(x+y)³-3(x+y)(x²+y²)+2(x³+y³)

=x³+3x²y+3xy²+y³-3x³-3y³-3x²y-3xy²+2x³+2y³=0

d)đang tìm hướng giải

đưa về HĐT rồi thay vài tính

a) y³ + 12y² + 48y + 64

= (y + 4)(y² - 4y + 16) + 12y(y + 4)

= (y + 4)(y² - 4y + 16 + 12y)

= (y + 4)(y² + 8y + 16)

= (y + 4)(y + 4)²

= (y + 4)³

b) y³ - 6y² + 12y - 8

= (y - 2)(y² + 2y + 4) - 6y(y - 2)

= (y - 2)(y² + 2y + 4 - 6y)

= (y - 2)(y² - 4y + 4)

= (y - 2)(y - 2)²

= (y - 2)³

a; y^3 + 12y^2 + 48y + 46 

= y^3 + 3 . 4 . y^2 + 3 . 16 . y + 64 - 18

= ( y + 8 )^3 - 18

= ( 6 + 8)^3 - 18 

= 14^3 - 18 

Cái 46 phải là 64 thì phải 

b, = ( y - 2)^3 = ( 22 - 2 )^3 = 20^3 = 8000