\(D=x^2+2xy+y^2-6x-6y-15\)

\(=\left(x+y\right)^2-6\left(x+y\right)-15=-9^2-6\cdot\left(-9\right)-15=120\)

\(D=x^2+2xy+y^2-6x-6y-15\)

\(=\left(x^2+2xy+y^2\right)-\left(6x+6y\right)-15\)

\(=\left(x+y\right)^2-6\left(x+y\right)-15\)

\(=\left(x+y\right)\left(x+y-6\right)-15\)

\(=\left(-9\right)\left(-9-6\right)-15\)

\(=120\)

D=x²+2xy+y²-6x-6y-15

D=(x^2+2xy+y^2)-(6x+6y)-15

D=(x+y)^2 - 6(x+y) - 15

D=(x+y)(x+y-6-15)

D= 9 . 9 - (-21)

D= 102

\(A=x^2+2xy+y^2-6-6y-5=\left(x+y\right)^2-6\left(x+y\right)-5=2^2-6\cdot2-5=-13\)

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

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

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

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

a) \(6x-6y=6\left(x-y\right)\)

b)\(2xy+3x+6y+xz\)

\(=\left(2xy+xz\right)+\left(6y+3z\right)\)

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

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

c)\(x^2+6x+9-y^2\)

\(=\left(x^2+6x+9\right)-y^2\)

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

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

d) \(9x-x^3\)

\(=x\left(9-x^2\right)\)

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

e)\(x^2-xy+x-y\)

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

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

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

a, 6x - 6y = 6( x-y )

b, 2xy + 3z + 6y + xz

  = ( 2xy + 6y ) + ( 3z + xz )

  = 2y( x + 3 ) + z ( 3 + x )

  = 2y( 3 + x ) + z ( 3 + x )

  = ( 3 + x ) ( 2y + z )

c, x² + 6x + 9 - y² = ( x² + 6x + 9 ) - y²

                             = ( x + 3 )² - y²

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

d , 9x - x³ = x ( 9 - x² )

                = x ( 3 - x ) ( 3 + x )

e, x² - xy + x - y =( x ² - xy ) + ( x - y )

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

                          = ( x - y ) ( x + 1 )

\(a,6x-6y=6\left(x-y\right)\)

\(b.2xy+3z+6y+xz\)

\(2y\left(x+3\right)+z\left(x+3\right)\)

\(\left(2y+z\right)\left(x+3\right)\)

\(c,x^2+6x+9-y^2\)

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

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

\(d,9x-x^3\)

\(x\left(9-x^2\right)\)

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

\(e,x^2-xy+x-y\)

\(x\left(x+1\right)-y\left(x+1\right)\)

\(\left(x+1\right)\left(x-y\right)\)

Điều kiện: \(y\ge0\)

pt thứ nhất của hệ \(\Leftrightarrow\left(y-x+3\right)^2=0\) \(\Leftrightarrow y-x+3=0\) \(\Leftrightarrow y=x-3\)

Thay vào pt thứ hai của hệ, ta được  \(2x^2+3x+x-3-\left(3x+1\right)\sqrt{x-3}-2=0\)

\(\Leftrightarrow2x^2+4x-5=\left(3x+1\right)\sqrt{x-3}\)         \(\left(x\ge3\right)\)

\(\Rightarrow\left(2x^2+4x-5\right)^2=\left[\left(3x+1\right)\sqrt{x-3}\right]^2\)

\(\Leftrightarrow4x^4+16x^2+25+16x^3-20x^2-40x=\left(3x+1\right)^2\left(x-3\right)\)

\(\Leftrightarrow4x^4+16x^3-4x^2-40x+25=9x^3-21x^2-17x-3\)

\(\Leftrightarrow4x^4+7x^3+17x^2-23x+28=0\)

Đặt \(f\left(x\right)=4x^4+7x^3+17x^2-23x+28\)

\(f\left(x\right)=4x^4+7x^3+17x^2+4+4+...+4-23x+4\) (có 6 số 4 ở giữa)

\(f\left(x\right)\ge9\sqrt[9]{4x^4.7x^3.17x^2.4^6}-23x+4\) \(=\left(9\sqrt[9]{1949696}-23\right)x+4\)

Hiển nhiên \(9\sqrt[9]{1949696}>23\). Lại có \(x\ge3\) nên \(f\left(x\right)>0\), Như vậy pt \(f\left(x\right)=0\) vô nghiệm. Điều đó có nghĩa là phương trình đã cho vô nghiệm.