8x³ + 27x³ + 4x² + 9y² - 6xy

= (2x + 3y)(4x² - 6xy + 9y²) + (4x² - 6xy +9y²)

= (4x² - 6xy + 9y²)(2x + 3y + 1)

Không chắc lắm

a) x² + xy + y - 1 = (x² - 1) + (xy + y) = (x - 1)(x + 1) + y(x + 1) = (x + 1)(x + y - 1)

b) 4 - x² + 2xy - y² = 4 - (x² - 2xy + y²) = 4 - (x - y)² = (x - y + 2)(4 - x + y) 

c) 8x² - 18y² = 2(4x² - 9y²) = 2[(2x)² - (3y)²] = 2(2x - 3y)(2x + 3y)

d) 8x³ - 4x² - 6xy - 9y² - 27y³

= (8x³ - 27y³) - (4x² + 6xy + 9y²)

= (2x - 3y)(4x² + 6xy + 9y²) - (4x² + 6xy + 9y²)

= (2x - 3y - 1)(4x² + 6xy + 9y²)

e) 4x² - x - 3 = 4x² - 4x + 3x - 3 = 4x(x - 1) + 3(x - 1) = (x - 1)(4x + 3)

f) 4x² - 8x + 3 = 4x² - 2x - 6x + 3 = 2x(2x - 1) - 3(2x - 1) = (2x - 3)(2x - 1)

cảm ơn bạn

a) 9x⁴+16y⁶-24x²y³

=(3x²)²-2.3x².4y³+(4y³)²

=(3x²-4y³)²

b) 16x²-24xy+9y²

=(4x)²-2.4x.3y+(3y)²

=(4x-3y)²

c) 36x²-(3x-2)²

=(36x-3x+2)(36x+3x-2)

=(33x+2)(39x-2)

d) 27x³+54x²y+36xy²+8y³

=(3x)³+3.(3x)².2y+3.3x.(2y)²+(2y)³

=(3x+2y)³

e) y⁹-9x²y⁶+27x⁴y³-27x⁶

=(y³)³-3.(y³)².3x²+3.y³.(3x²)²-(3x²)³

=(y³-3x²)³

f) 64x³+1

= (4x)³+1³

=(4x+1)[(4x)²-4x.1+1²]

=(4x+1)(16x²-4x+1)

e) 27x⁶-8x³  *sửa đề*

=(3x²)³-(2x)³

=(3x²-2x)[(3x)²+3x².2x+(2x)²]

=(3x²-2x)(9x²+6x³+4x²)

~~~

a) \(-x^3+9x^2-27x+27=-\left(x^3-3.3.x^2+3.3^2.x-3^3\right)=-\left(x-3\right)^3\)

b)\(x^4-2x^3-x^2+2x+1=x^4+\left(-x\right)^2+\left(-1\right)^2+2x^2\left(-x\right)+2.\left(-x\right).\left(-1\right)+2x^2.\left(-1\right)\)

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

c)\(8x^3+27y^3+36x^2y+54xy^2=\left(2x\right)^3+3.\left(2x\right)^2.3y+3.2x.\left(3y\right)^2+\left(3y\right)^3\)

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

\(27y^3-9y^2+y-\frac{1}{27}\)

\(=\left(3y\right)^3-3.\left(3y\right)^2.\frac{1}{3}+3.3y.\left(\frac{1}{3}\right)^2-\left(\frac{1}{3}\right)^3\)

\(=\left(3y-\frac{1}{3}\right)^3\)

hk

tốt

\(8x^3+36x^2y+54xy^2+27y^3\\ =\left(2x\right)^3+3.\left(2x\right)^2.3y+3.2x.\left(3y\right)^2+\left(3y\right)^3\\ =\left(2x+3y\right)^3\\ =\left(2x+3y\right)\left(2x+3y\right)\left(2x+3y\right)\)

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

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

\(\left(x-1\right)^2-\left(x+1\right)^2\\ =\left(x-1-x-1\right)\left(x-1+x+1\right)\\ =-2.2x=-4x\)

a: =(2x)^3+3*(2x)^2*3y+3*2x*(3y)^2+(3y)^3

=(2x+3y)^3

b: (x-y)^3-(x+y)^3

=(x-y-x-y)[(x-y)^2+(x-y)(x+y)+(x+y)^2]

=-2y*[x^2-2xy+y^2+x^2-y^2+x^2+2xy+y^2]

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

c: (x+1)^3+(x-1)^3

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

=2x*[x^2+2x+1-x^2+1+x^2-2x+1]

=2x(x^2+3)

d: =(x-1-x-1)(x-1+x+1)

=2x*(-2)=-4x

\(8x^3+36x^2y+54xy^2+27y^3\)

\(=\left(2x\right)^3+3.\left(2x\right)^2.3y+3.2x.\left(3y\right)^2+\left(3y\right)^3\)

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

\(------\)

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

\(=\left(x-y-x-y\right)\left[\left(x-y\right)^2+\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2\right]\)

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

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

\(------\)

\(\left(x+1\right)^3+\left(x-1\right)^3\)

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

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

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

\(------\)

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

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

\(=-2.2x=-4x\)

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

b)  \(8x^3+12x^2+6x+1=\left(2x+1\right)^3\)

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

\(=\left(2y-2x\right)\left(2y+2x-2\right)=4\left(y-x\right)\left(y+x-1\right)\)

\(8x^3-36x^2y+54xy^2-27y^3\)

\(=\left(2x\right)^3-3.\left(2x\right)^2.3y+3.2x.\left(3y\right)^2-\left(3y\right)^3\)

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

\(8x^3-36x^2y+54xy^2-27y^3\)

\(=\left(2x\right)^3-3.\left(2x\right)^2.3y+3.2x.\left(3y\right)^2-\left(3y^3\right)\)

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

Bài trên là hằng đẳng thức:

\(\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3\)

8x³ - 36x²y  + 54xy² - 27y³

= (2x)³ - 3.(2x)².3y -3.2x.(3y)² + (3y)³

= (2x - 3y)³