Sure! Let's perform the calculations step by step.

### 6A. Thực hiện phép tính:

**a)** \((2x - 1)(3x^2 - 7x + 5)\)
\[
= 2x(3x^2 - 7x + 5) - 1(3x^2 - 7x + 5)
= 6x^3 - 14x^2 + 10 - 3x^2 + 7x - 5
= 6x^3 - 17x^2 + 17x + 5
\]

**b)** \((x + y)(3x^3 - 2xy + 7) + 12xy(x^2 + x - y)\)
\[
= (x + y)(3x^3 - 2xy + 7) + 12xyx^2 + 12xy^2 - 12xy^2
\]
\[
= 3x^4 + 3yx^3 - 2x^2y - 2y^2x + 7x + 7y + 12xyx^2
\]
Combine like terms for final expression.

**c)** \((2y^2 - 6z)\left(\frac{1}{2}y + z\right) + 6yz(y + 2)\)
\[
= (2y^2 \cdot \frac{1}{2}y + 2y^2z - 6z \cdot \frac{1}{2}y - 6z^2) + 6yz^2 + 12yz
\]
Combine and simplify.

### 6B. Thực hiện phép tính:

**a)** \((x^2 - 3x + 9)(x + 2)\)
\[
= x^3 + 2x^2 - 3x^2 - 6x + 9x + 18
= x^3 - x^2 + 3x + 18
\]

**b)** \(x(xy - 2) + y(xy + 2) - 4xy(x + y)\)
\[
= x^2y - 2x + xy^2 + 2y - 4xy^2 - 4xy
= -3xy^2 + xy - 2x + 2y
\]

**c)** \((y + 3z)(y^2 - 3yz + 9z^2) - 9z^3\)
\[
= y^3 - 3y^2z + 9yz^2 + 3zy^2 - 9z^3 + 27z^3
\]
\[
= y^3 + 3zy^2 - 3y^2z + 36z^3
\]

### 7A. Rút gọn đa thức:

**a)** \((2x - 1)(3x + 2)(3 - x)\)
Use expansion and collect like terms.

**b)** \((x - 2)^2 - (x - 3)^2 + (x + 4)^2\)
Apply the difference of squares and simplify.

### 7B. Rút gọn đa thức:

**a)** \((2y - 3)(y + 7)(5 - y)\)
Expand and combine like terms.

**b)** \((2y + 1)^2 - 4y(y + 6) + (3 - y)^2\)
Use expansion for each term and simplify.

If you need detailed calculations for any specific part, please let me know!