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

b: \(x^3+8y^3=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)

c: \(x^3+125=\left(x+5\right)\left(x^2-5x+25\right)\)

d: \(x^3-27y^3=\left(x-3y\right)\left(x^2+3xy+9y^2\right)\)

a) 8x³ - 1

= (2x)³ - 1³

= (2x - 1)(4x² + 2x + 1)

b) x³ + 8y³

= x³ + (2y)³

= (x + 2y)(x² + 2xy + 4y²)

c) x³ + 125

= x³ + 5³

= (x + 5)(x² - 5x + 25)

d) x³ - 27y³

= x³ - (3y)³

= (x - 3y)(x² + 3xy + 9y²)

 Chúc bạn học tốt

a. 8x³ - 1

⇔ (2x)³ - 1³

⇔ (2x - 1)³.

b. x³ + 8y³

⇔ x³ + (2y)³

⇔ (x + 2y)³

c. x³ + 125

⇔ x³ + 5³

⇔ (x + 5)³

d. x³ - 27y³

⇔ x³ - (3y)³

⇔ (x - 3y)³

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

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

c: \(\dfrac{1}{8}x^3-\dfrac{9}{4}x^2y+\dfrac{27}{2}xy^2-27y^3=\left(\dfrac{1}{2}x-3y\right)^3\)

b: \(-x^3+12x^2-48x+64=\left(-x+4\right)^3\)

a) Ta có: \(1+6x-6x^2-x^3\)

\(=\left(1-x\right)\left(x^2+x+1\right)+6x\left(1-x\right)\)

\(=\left(1-x\right)\left(x^2+7x+1\right)\)

b:Ta có: \(x^3-4x^2+8x-8\)

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

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

c: Ta có: \(x^3+2x^2+2x+1\)

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

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

d: Ta có: \(8x^3-12x^2+6x-1\)

\(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2-1^3\)

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

a: =(x-1)^3

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

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

=(x-y)^3

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

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

c: \(8x^3+y^3=\left(2x+y\right)\left(4x^2-2xy+y^2\right)\)

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

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

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

a) \(M=x^2-100=\left(x-10\right)\left(x+10\right)\)

b) \(N=x^3+1000=\left(x+10\right)\left(x^2-10x+100\right)\)

c) \(125x^3-1=\left(5x-1\right)\left(25x^2+5x+1\right)\)

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

a, \(M=x^2-100=\left(x-10\right)\left(x+10\right)\)

b, \(N=x^3+1000=\left(x+10\right)\left(x^2-10x+100\right)\)

c, \(P=125x^3-1=\left(5x-1\right)\left(25x^2+5x+1\right)\)

d, \(Q=8x^3-27=\left(2x-3\right)\left(2x+3\right)\)