Dưới đây là kết quả cho biểu thức mà bạn đã cung cấp:

### a) \((x + 2) \times (x^2 - 2x + 4) - x^2 + 2\)

**Bước 1:** Thực hiện nhân hai biểu thức đầu tiên:

\[
(x + 2)(x^2 - 2x + 4) = x(x^2 - 2x + 4) + 2(x^2 - 2x + 4)
\]
\[
= x^3 - 2x^2 4x + 2x^2 - 4x + 8 = x^3 + 8
\]

**Bước 2:** Thay vào và tính:

\[
x^3 + 8 - x^2 + 2 = x^3 - x^2 + 10
\]

**Kết quả:**
\[
x^3 - x^2 + 10
\]

---

### b) \((x - 1) \times (x^2 + x + 1) - (x + 1) \times (x^2 - x + 1)\)

**Bước 1:** Tính từng phần:

\[
(x - 1)(x^2 + x + 1) = x^3 + x^2 + x - x^2 - x - 1 = x^3 - 1
\]
\[
(x + 1)(x^2 - x + 1) = x^3 - x^2 + x + x^2 - x + 1 = x^3 + 1
\]

**Bước 2:** Thay vào và tính:

\[
(x^3 - 1) - (x^3 + 1) = x^3 - 1 - x^3 - 1 = -2
\]

**Kết quả:**
\[
-2
\]

---

### c) \((7x + 4)^2 - (7x + 4) \times (7x - 4)\)

**Bước 1:** Tính từng phần:

\[
(7x + 4)^2 = 49x^2 + 56x + 16
\]
\[
(7x + 4)(7x - 4) = 49x^2 - 28x + 28x - 16 = 49x^2 - 16
\]

**Bước 2:** Thay vào và tính:

\[
(49x^2 + 56x + 16) - (49x^2 - 16) = 49x^2 + 56x + 16 - 49x^2 + 16 = 56x + 32
\]

**Kết quả:**
\[
56x + 32
\]

---

### d) \((3x + y)(9x^2 - 3xy + y^2) - (3x - y)^3 - 27x^2y\)

**Bước 1:** Tính từng phần:

1. **Phần đầu tiên:**
\[
(3x + y)(9x^2 - 3xy + y^2) = 3x(9x^2 - 3xy + y^2) + y(9x^2 - 3xy + y^2)
\]
\[
= 27x^3 - 9x^2y + 3xy^2 + 9xy^2 - 3y^3 = 27x^3 - 9x^2y + 12xy^2 - 3y^3
\]

2. **Phần hai:**
\[
(3x - y)^3 = 27x^3 - 27x^2y + 9xy^2 - y^3
\]

3. **Tính cả phần:**
\[
(3x+y)(9x^2 - 3xy + y^2) - (3x - y)^3 - 27x^2y = (27x^3 - 9x^2y + 12xy^2 - 3y^3) - (27x^3 - 27x^2y + 9xy^2 - y^3) - 27x^2y
\]

**Bước 2:** Giản ước:

\[
= 27x^3 - 9x^2y + 12xy^2 - 3y^3 - 27x^3 + 27x^2y - 9xy^2 + y^3 - 27x^2y
\]
\[
= 27x^3 - 27x^3 + (-9x^2y + 27x^2y - 27x^2y) + (12xy^2 - 9xy^2) + (-3y^3 + y^3)
\]
\[
= 0 + 3xy^2 - 2y^3
\]

**Kết quả:**
\[
3xy^2 - 2y^3
\]

---

Tóm lại, các kết quả là:
- a) \(x^3 - x^2 + 10\)
- b) \(-2\)
- c) \(56x + 32\)
- d) \(3xy^2 - 2y^3\)

Let's simplify each of these expressions step by step.

a. (x+2)×(x2−2x+4)−x2+2(x+2) \times (x^2 - 2x + 4) - x^2 + 2(x+2)×(x2−2x+4)−x2+2
Expand (x+2)×(x2−2x+4)(x+2) \times (x^2 - 2x + 4)(x+2)×(x2−2x+4):

(x+2)(x2−2x+4)=x(x2−2x+4)+2(x2−2x+4)(x+2)(x^2 - 2x + 4) = x(x^2 - 2x + 4) + 2(x^2 - 2x + 4)(x+2)(x2−2x+4)=x(x2−2x+4)+2(x2−2x+4) =x3−2x2+4x+2x2−4x+8= x^3 - 2x^2 + 4x + 2x^2 - 4x + 8=x3−2x2+4x+2x2−4x+8 =x3+8= x^3 + 8=x3+8
Subtract x2−2x^2 - 2x2−2:

x3+8−x2+2=x3−x2+10x^3 + 8 - x^2 + 2 = x^3 - x^2 + 10x3+8−x2+2=x3−x2+10
So, the simplified expression for part (a) is:

x3−x2+10x^3 - x^2 + 10x3−x2+10b. (x−1)×(x2+x+1)−(x+1)×(x2−x+1)(x-1) \times (x^2 + x + 1) - (x+1) \times (x^2 - x + 1)(x−1)×(x2+x+1)−(x+1)×(x2−x+1)
Expand (x−1)×(x2+x+1)(x-1) \times (x^2 + x + 1)(x−1)×(x2+x+1):

(x−1)(x2+x+1)=x(x2+x+1)−1(x2+x+1)(x-1)(x^2 + x + 1) = x(x^2 + x + 1) - 1(x^2 + x + 1)(x−1)(x2+x+1)=x(x2+x+1)−1(x2+x+1) =x3+x2+x−x2−x−1= x^3 + x^2 + x - x^2 - x - 1=x3+x2+x−x2−x−1 =x3−1= x^3 - 1=x3−1
Expand (x+1)×(x2−x+1)(x+1) \times (x^2 - x + 1)(x+1)×(x2−x+1):

(x+1)(x2−x+1)=x(x2−x+1)+1(x2−x+1)(x+1)(x^2 - x + 1) = x(x^2 - x + 1) + 1(x^2 - x + 1)(x+1)(x2−x+1)=x(x2−x+1)+1(x2−x+1) =x3−x2+x+x2−x+1= x^3 - x^2 + x + x^2 - x + 1=x3−x2+x+x2−x+1 =x3+1= x^3 + 1=x3+1
Subtract the second expansion from the first:

(x3−1)−(x3+1)=x3−1−x3−1(x^3 - 1) - (x^3 + 1) = x^3 - 1 - x^3 - 1(x3−1)−(x3+1)=x3−1−x3−1 =−2= -2=−2
So, the simplified expression for part (b) is:

−2-2−2c. (7x+4)2−(7x+4)×(7x−4)(7x + 4)^2 - (7x + 4) \times (7x - 4)(7x+4)2−(7x+4)×(7x−4)
Expand (7x+4)2(7x + 4)^2(7x+4)2:

(7x+4)2=(7x)2+2⋅7x⋅4+42(7x + 4)^2 = (7x)^2 + 2 \cdot 7x \cdot 4 + 4^2(7x+4)2=(7x)2+2⋅7x⋅4+42 =49x2+56x+16= 49x^2 + 56x + 16=49x2+56x+16
Expand (7x+4)×(7x−4)(7x + 4) \times (7x - 4)(7x+4)×(7x−4):

(7x+4)(7x−4)=7x⋅7x+7x⋅(−4)+4⋅7x+4⋅(−4)(7x + 4)(7x - 4) = 7x \cdot 7x + 7x \cdot (-4) + 4 \cdot 7x + 4 \cdot (-4)(7x+4)(7x−4)=7x⋅7x+7x⋅(−4)+4⋅7x+4⋅(−4) =49x2−28x+28x−16= 49x^2 - 28x + 28x - 16=49x2−28x+28x−16 =49x2−16= 49x^2 - 16=49x2−16
Subtract the second expansion from the first:

(49x2+56x+16)−(49x2−16)=49x2+56x+16−49x2+16(49x^2 + 56x + 16) - (49x^2 - 16) = 49x^2 + 56x + 16 - 49x^2 + 16(49x2+56x+16)−(49x2−16)=49x2+56x+16−49x2+16 =56x+32= 56x + 32=56x+32
So, the simplified expression for part (c) is:

56x+3256x + 3256x+32d. (3x+y)×(9x2−3xy+y2)−(3x−y)3−27x2y(3x + y) \times (9x^2 - 3xy + y^2) - (3x - y)^3 - 27x^2y(3x+y)×(9x2−3xy+y2)−(3x−y)3−27x2y
Expand (3x+y)×(9x2−3xy+y2)(3x + y) \times (9x^2 - 3xy + y^2)(3x+y)×(9x2−3xy+y2):

(3x+y)(9x2−3xy+y2)=3x⋅9x2+3x⋅(−3xy)+3x⋅y2+y⋅9x2+y⋅(−3xy)+y⋅y2(3x + y)(9x^2 - 3xy + y^2) = 3x \cdot 9x^2 + 3x \cdot (-3xy) + 3x \cdot y^2 + y \cdot 9x^2 + y \cdot (-3xy) + y \cdot y^2(3x+y)(9x2−3xy+y2)=3x⋅9x2+3x⋅(−3xy)+3x⋅y2+y⋅9x2+y⋅(−3xy)+y⋅y2 =27x3−9x2y+3xy2+9x2y−3xy2+y3= 27x^3 - 9x^2y + 3xy^2 + 9x^2y - 3xy^2 + y^3=27x3−9x2y+3xy2+9x2y−3xy2+y3 =27x3+y3= 27x^3 + y^3=27x3+y3
Expand (3x−y)3(3x - y)^3(3x−y)3:

(3x−y)3=(3x−y)(3x−y)(3x−y)(3x - y)^3 = (3x - y)(3x - y)(3x - y)(3x−y)3=(3x−y)(3x−y)(3x−y)Using binomial expansion:

(3x−y)2=9x2−6xy+y2(3x - y)^2 = 9x^2 - 6xy + y^2(3x−y)2=9x2−6xy+y2 (3x−y)3=(3x−y)(9x2−6xy+y2)(3x - y)^3 = (3x - y)(9x^2 - 6xy + y^2)(3x−y)3=(3x−y)(9x2−6xy+y2) =3x⋅9x2−3x⋅6xy+3x⋅y2−y⋅9x2+y⋅6xy−y⋅y2= 3x \cdot 9x^2 - 3x \cdot 6xy + 3x \cdot y^2 - y \cdot 9x^2 + y \cdot 6xy - y \cdot y^2=3x⋅9x2−3x⋅6xy+3x⋅y2−y⋅9x2+y⋅6xy−y⋅y2 =27x3−18x2y+3xy2−9x2y+6xy2−y3= 27x^3 - 18x^2y + 3xy^2 - 9x^2y + 6xy^2 - y^3=27x3−18x2y+3xy2−9x2y+6xy2−y3 =27x3−27x2y+9xy2−y3= 27x^3 - 27x^2y + 9xy^2 - y^3=27x3−27x2y+9xy2−y3
Subtract (3x−y)3(3x - y)^3(3x−y)3 and 27x2y27x^2y27x2y from the first expansion:

(27x3+y3)−(27x3−27x2y+9xy2−y3)−27x2y(27x^3 + y^3) - (27x^3 - 27x^2y + 9xy^2 - y^3) - 27x^2y(27x3+y3)−(27x3−27x2y+9xy2−y3)−27x2y =27x3+y3−27x3+27x2y−9xy2+y3−27x2y= 27x^3 + y^3 - 27x^3 + 27x^2y - 9xy^2 + y^3 - 27x^2y=27x3+y3−27x3+27x2y−9xy2+y3−27x2y =2y3−9xy2= 2y^3 - 9xy^2=2y3−9xy2
So, the simplified expression for part (d) is:

2y3−9xy22y^3 - 9xy^22y3−9xy2