A) \(x^3+27\)

\(=x^3+3^3\)

\(=\left(x+3\right)\left(x^2-3x+9\right)\)

B) \(x^3-\dfrac{1}{8}\)

\(=x^3-\left(\dfrac{1}{2}\right)^3\)

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

C) \(8x^3+y^3\)

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

\(=\left(2x+y\right)\left(4x^2-2xy+y^2\right)\)

D) \(8x^3-27y^3\)

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

\(=\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)\)

a)\(\left(x+3\right)\left(x^2-3x+9\right)\)

b)\(\left(x-\dfrac{1}{2}\right)\left(x^2+\dfrac{1}{2}x+\dfrac{1}{4}\right)\)

c)\(\left(2x+y\right)\left(4x^2-2xy+y^2\right)\)

d)\(\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)\)

a: =(x-1)^3

b: =(-2x+1)^3

c: =x^3-3x^2y+3xy^2-y^3

=(x-y)^3

a) x^3 + 8 = x^3 + 2^3 = (x+2)(x^2-2x+2)

b) 27-8y^3 =3^3-(2y)^3=(3-2y)(3^2+2*3Y+8y^3)

c) y^6+1= (y^2)^3+1^3 = (y^2+1)(Y^6+ y^2+ 1)

bài này áp dụng hằng đẳng thức đáng nhớ bạn nhé

a) \(x^3+8=\left(x+2\right)\cdot\left(x^2-2x+4\right)\)

b) \(27-8y^3=\left(3-2y\right)\left(9+6y+4y^2\right)\)

c) \(y^6+1=\left(y^2+1\right)\left(y^4-y^2+1\right)\)

a: x^3+8=(x+2)(x^2-2x+4)

b: =(3x+1)(9x^2-3x+1)

c: =(x+3)(x^2-3x+9)

d: =(4x-3y)(16x^2+24xy+9y^2)

\(a.x^3+8=\left(x+2\right)\left(x^2-2x+4\right)\) 

\(b.27x^3+1=\left(3x+1\right)\left(9x-3x+1\right)\)

\(c.x^3+27=\left(x+3\right)\left(x^2-3x+9\right)\) 

\(d.64x^3-27y^3=\left(4x-3y\right)\left(16x^2+12xy+9y^2\right)\)  

a: \(1-\dfrac{x^3}{8}=\left(1-\dfrac{1}{2}x\right)\left(1+\dfrac{1}{2}x+\dfrac{1}{4}x^2\right)\)

b: \(27x^3+1=\left(3x+1\right)\left(9x^2-3x+1\right)\)

c: \(64x^3-27y^3=\left(4x-3y\right)\left(16x^2+12xy+9y^2\right)\)

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

e, x⁴ - 2x³ + x² 

= x²( x²  - 2x + 1)  

= x² (x - 1)²

e: \(x^4-2x^3+x^2\)

\(=x^2\cdot x^2-x^2\cdot2x+x^2\cdot1\)

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

\(=x^2\left(x-1\right)^2\)

f: \(27y^3-x^3\)

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

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

Bài 5

a) A = -x³ + 6x² - 12x + 8

= -x³ + 3.(-x)².2 - 3.x.2² + 2³

= (-x + 2)³

= (2 - x)³

Thay x = -28 vào A ta được:

A = [2 - (-28)]³

= 30³

= 27000

b) B = 8x³ + 12x² + 6x + 1

= (2x)³ + 3.(2x)².1 + 3.2x.1² + 1³

= (2x + 1)³

Thay x = 1/2 vào B ta được:

B = (2.1/2 + 1)³

= 2³

= 8

Bài 6

a) 11³ - 1 = 11³ - 1³

= (11 - 1)(11² + 11.1 + 1²)

= 10.(121 + 11 + 1)

= 10.133

= 1330

b) Đặt B =  x³ - y³ = (x - y)(x² + xy + y²)

= (x - y)(x² - 2xy + y² + 3xy)

= (x - y)[(x - y)² + 3xy]

Thay x - y = 6 và xy = 9 vào B ta được:

B = 6.(6² + 3.9)

= 6.(36 + 27)

= 6.63

= 378

Bài 6 :

a) \(11^3-1=\left(11-1\right)\left(11^2+11+1^2\right)\)

\(\)\(=10.\left(121+12\right)\)

\(=10.133\)

\(=1330\)

b) \(\left\{{}\begin{matrix}x-y=6\\xy=9\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2+y^2-2xy=36\\xy=9\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2+y^2-2.18=36\\xy=9\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2+y^2=72\\xy=9\end{matrix}\right.\)

Ta có :

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

\(=6.\left(72+9\right)\)

\(=6.81\)

\(=486\)

a)8x3 + * + * + 27y3 = (* + *)3

=>A=(2x+3y)^3

b) (2x+1)^3

c)(x-2y)^3

d)(3x-2)(3x+2)

e)(3x-1)(9x^2+3x+1)

f)....................

6: \(27x^3+1=\left(3x+1\right)\left(9x^2-3x+1\right)\)

7: \(\left(2x+1\right)^2=4x^2+4x+1\)

8: \(\left(2x-1\right)^2=4x^2-4x+1\)

9: \(9-16x^2=\left(3-4x\right)\left(3+4x\right)\)