\(P=\left(2x-y\right)^3+3\left(2x-y\right)+12x^2+3y^2+11\)

\(=9^3+3\cdot9+3\left(4x^2+y^2\right)+11\)

\(=119+3\left[4x^2+y^2+4xy-4xy\right]\)

\(=119+3\cdot\left[\left(2x-y\right)^2+4xy\right]\)

\(=119+3\cdot\left[9^2+4xy\right]\)

\(=119+243+12xy\)

\(=362+12xy\)

\(A=8x^3+12x^2y+6xy^2+y^3=27\)

\(\Leftrightarrow\left(2x+y\right)^3=27\)

=>2x+y=3

\(B=x\left(2x+y\right)+xy+\dfrac{1}{2}y^2\)

\(=3x+\dfrac{1}{2}y\left(2x+y\right)=3x+\dfrac{1}{2}y\cdot3=3x+\dfrac{3}{2}y\)

\(=\dfrac{3}{2}\left(2x+y\right)=\dfrac{3}{2}\cdot3=\dfrac{9}{2}\)

`8x^3 - 12x^{2} y + 6xy^2 - y^3 + 12x^2 - 12xy + 3y^2 + 11`

`=(8x^3 - 12x^{2}y + 6xy^{2} - y^{3}) + 3(4x^2 - 4xy + y^2) + 11`

`=(2x-y)^{3} + 3(2x-y)^2 + 11`

Thay `2x-y=9` vào `:`

`9^3 + 3 . 9^2 + 11`

`=729 + 243 + 11`

`=983`

A=8x^3-12x^2y+6xy^2-y^3+12x^2-12xy+3y^2+11

=(2x-y)^3+4(2x-y)^2+11

Khi 2x-y=9 thì A=9^3+4*9^2+11

=1064

Ta có:

\(8x^3-12x^2y+6xy^2-y^3\)

\(=\left(2x\right)^3-3.4.x^2.y+3.2.x.y^2-y^3=\left(2x-y\right)^3\) (hằng đẳng thức : \(\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3\) )

Thay y=2x+5 vào biểu thức,ta đc:

\(\left[2x-\left(2x+5\right)\right]^3=\left(2x-2x-5\right)^3=\left(-5\right)^3=-125\)

Vậy giá trị của biểu thức .... là -125 khi y=2x+5